The identification of dark matter : proceedings of the third international workshop, York, U.K., 18-22 September 2000 9789812811363, 9812811362

Table of contents :
Part 1 Dark matter in the universe - theory and observation: the early universe, nucleosynthesis and cosmology
cosmic microwave background radiation
large scale structure
halos, halo models and dark matter
particle physics and supersymmetry. Part 2 Baryonic searches: introduction to baryonic dark matter searches
direct observational evidence for baryonic dark matter
microlensing evidence for dark matter
next generation astronomical searches. Part 3 Non-baryonic searches: introduction to non-baryonic dark matter searches
WIMP detectors
WIMP detectors with directional sensitivity and future prospects
axion detectors
WIMP detection by indirect techniques
neutrino dark matter searches
next generation neutrino, WIMP and axion techniques
implications for astrophysical neutrino detection.

Citation preview

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edited by

Neil J. C. Spooner Vitaly Kudryavtsev World Scientific

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T H E

IDENTIFICATION OF

DARK MATTER

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Proceedings of the Third International Workshop on

THE

IDENTIFICATION OF

DARK MATTER

York, U K

18-22 September 2000

edited by

Neil J. C. Spooner Vitaly Kudryavtsev U n i v e r s i t y of

Sheffield

World Scientific l M

Sinaaoore* Singapore

»New New Jersey

•*L London* Hong

Kong

Published

by

World Scientific Publishing Co. Pie. Lid. P O B o x 128, Fairer Road, Singapore 912805 USA office: UK office:

Suite IB. 1060 Main Street, River Edge, NJ 07661 57 Shelton Street. Covent Garden, London WC2H 9HE

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.

Cover I l l u s t r a t i o n : Internal view of veto system for xenon dark matter detector, courtesy of Igor Liubarsky (the UK Dark Matter Collaboration).

THE

IDENTIFICATION O F DARK M A T T E R

Copyright © 2001 by World Scientific Publishing Co. Pte. Ltd. A l l rights reserved. This book, or parts thereof, may not be reproduced in any f o r m or by any means, electronic or mechanical, i n c l u d i n g photocopying, recording or any i n f o r m a t i o n storage and r e t r i e v a l system now known or to be invented, without written permission f r o m the Publisher.

For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc.. 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.

ISBN 981-02-4602-1

Printed in Singapore.

Preface

This book contains written versions of the presentations made at the 3rd International W o r k s h o p on the Identification o f Dark Matter ( I D M 2 0 0 0 ) held in York, U K on 18th to 22nd September 2000. The objective o f the I d e n t i f i c a t i o n o f D a r k M a t t e r workshop series, started i n 1996 with a meeting in Sheffield ( I D M 9 6 ) is to assess critically the status of work trying to i d e n t i f y what constitutes the dark matter i n the Universe. In particular, to consider what techniques, both observational and experimental, are currently being used; how successful these are and what new techniques are likely to improve prospects for identifying likely dark matter candidates i n the future. Special emphasis was placed on recent results obtained i n searches for baryonic and non-baryonic dark matter. F o l l o w i n g the format adopted at I D M 9 6 and I D M 9 8 the meeting included reviews on major particle astrophysics topics i n dark matter, but was largely devoted to short contributed talks. A general aim o f the workshop was to bring together in one dedicated meeting astronomers and particle physicists working specifically in the dark matter field. For instance, those working on microlensing searches for M A C H O s , direct and indirect searches for W I M P s , searches for axions, searches for Dark Matter candidates at accelerators, as well as many other areas. W e wanted "all-plenary" sessions where people presented original work or informed reviews o f the subject. This in fact was achieved, with astrophysics and particle physics sessions interleaved to provide an interdisciplinary atmosphere. Several social events were held as an antidote to the science. A reception was held at the National Railway M u s e u m in Y o r k and included a special tour. The workshop banquet was held at Merchant Adventurer's H a l l . A public talk was given by Lawrence Krauss i n the Yorkshire M u s e u m . Many thanks must go to the Sheffield Physics Department team for their strenuous efforts i n making the workshop run so smoothly. Particular thanks to L e e Thompson and John Roberts for running the finances and industrial exhibition. Sponsorship from the Particle Physics and Astronomy Research C o u n c i l and the companies who participated in the industrial exhibition was very welcome. Finally we thank all the delegates, without whom there would have been no workshop or proceedings.

N e i l Spooner

vi

International Scientific Committee L . Bergstrom (Stockholm)

F. Avignone (USC) R. Bernabei (Rome) D . Caldwell ( U C S B ) J . Carr (Marseille) J. Ellis (CERN) K . Freese (Michigan) G . G i l m o r e (Cambridge) W . Jones ( I C S T M ) H . Klapdor-Kleingrothaus (MPI) M . M i n o w a (Tokyo) P. Nath ( N E U ) L . R o s z k o w s k i (Lancaster) J . S i l k (Oxford) P- Smith ( R A L ) T . Sumner ( I C S T M )

A . Bottino (Torino) B. Carr(QMW) D . Cline ( U C L A ) C . Frenk (Durham) K . F u s h i m i (Tokushima) P. G o n d o l o ( M P G ) L . Krauss (Case Western) S. M a t s u k i ( K y o t o ) A . Morales (Zaragoza) J . Q u e n b y (IC) P. S i k i v i e (Florida) N . Smith ( R A L ) N . Spooner (Sheffield) K . V a n Bibber ( L L N L )

Local Organising Committee S. Cartwright P. Lightfoot J. M c M i l l a n J. Roberts N,Spooner D. Tovey

V. T. B. M. L.

Kudryavtsev Lawson Morgan Robinson Thompson

Session C h a i r m e n L . Bergstrom B.Carr D . Caldwell J . Quenby A . Incicchitti N . Smith

J. Peacock L . Krauss G . Gratta T . Sumner H . Kraus

Exhibiting Companies H i l g e r Crystals ltd. Electron Tubes L t d . Hytec Electronics L t d .

Southern Scientific L t d . LeCroy Ltd.

Contents

Preface

SESSION A . D A R K M A T T E R IN T H E U N I V E R S E — T H E O R Y AND O B S E R V A T I O N

Session A l :

The Early Universe, Nucleosynthesis and Cosmology

Space, Time and Matter: Cosmological Parameters 2001 L. M . Krauss

1

Cold Dark Matter M o d e l s and Q C. S. F r e n k f

Cosmological Parameters; D o W e Already K n o w the Final Answer M. Rowan-Robinson

20

Evidence from Type l a Supernovae for an Accelerating Universe A . G. Riess a n d A . V. F i S i p p e n k o (for t h e H i g h - Z S u p e r n o v a Search Team)

30

Dynamical Recovery o f Cosmological Constant S. C a p o z z i e l l o a n d G . L a m b i a s e

50

Large Extra Dimensions: Astrophysical Implications T. H a n 1

Session A2:

Cosmic Microwave Background Radiation

Observations of C o s m i c Background Radiation with M A X I M A P. Ferreira' Constraints on Dark Matter from the M i c r o w a v e Background and Large-Scale Structure /. A . P e a c o c k speaker ' contribution not received

VII

58

VIII Session A3:

Large Scale Structure

E U V and Soft X - R a y s from Clusters o f Galaxies — the 'Cluster So ft-Excess' Phenomenon M . Bonamente a n d R. L i e u

Session A4:

Halos, Halo Models, and Dark Matter

N o N e e d for Dark Matter in Galaxies? N . W. Evans M o d e l s o f the M i l k y W a y ' s Dark H a l o P. UUio

1

Directional Sensitivity, W I M P Detection, and the Galactic H a l o C. C o p i ' Caustics and C o l d Dark Matter B. M o o r e Deep Supernova Observations and the Nature o f Dark Matter Halos L Bergstrom', M .G o l i a t h , A . G o o b a r a n d E. M b r t s e l l Dark Matter Caustics P . S i k i v i e ' a n d W. K i n n e y Neutralino Dark Matter and Caustic R i n g Signals C. G u n n a r s s o n The Spherical Collapse M o d e l in a Universe with Cosmological Constant E . L . L o k a s a n d Y, H o f f m a n Dark Matter Detection in a Clumpy H a l o D . Stiff , L . M . W i d r o w a n d J. F r i e m a n

Session AS:

Particle Physics and Supersymmetry

A x i n o — N e w Candidate for C o l d Dark Matter L. Roszkowski

Recent Developments in Supersymmetric Dark Matter A . Corsetti a n d P. N a t h ' Precise Calculation o f Neutralino Relic Density in the M i n i m a l Supergravity M o d e l T. N i h e i M i r r o r Dark Matter R. N . M o h a p a i r a " a n d V. L . T e p l i t z The W I M P L i m i t from an Accelerator Experiment — Searches for Sfermions, Charginos and Neutralinos at A L E P H C. f t . B o o t h (for t h e A L E P H C o l l a b o r a t i o n ) S U S Y Searches with the DO Detector at Fermilab A . P . W h i t e (for t h e D O C o l l a b o r a t i o n )

SESSION B.

BARYONIC SEARCHES

Session BO:

Introduction to Baryonic Dark Matter Searches

Recent Developments in the Search for M A C H O s B. J. C a r r Death o f Stellar Baryonic Dark Matter K . F r e e z e , B , D . F i e l d s a n d D . S.

Session B l :

Graff

Direct Observational Evidence for Baryonic Dark Matter

Mass Beyond the M a i n Sequence H . R. A . Jones T i m e Dilation and the Nature o f Dark Matter M . R. S. H a w k i n s

Session B2:

Microlensing Evidence for Dark Matter

Dark Matter Distribution from the U H Weak Lensing Survey N. Kaiser'

X

E R O S Microlensing Results: Not Enough M A C H O s in the Galactic Halo E. A u b o u r g

238

The M A C H O Project 5.7 Y e a r L M C Results M . J . Lehnef, C. A l c o c k , R. A . A l l s m a n , D . R. A l v e s , T. S. A x e l r o d , A . C. Becker, D . P . Bennett, K.H . Cook, N . Dalai, A . J . D r a k e , K . C. F r e e m a n , M . G e h a , K . G r i e s t , S. L . M a r s h a l l , D . M i n n i t i , C. A . N e l s o n , B . A . P e t e r s o n , P . P o p o w s k i , M . R. P r a t t , P . J . Q u i n n , C. W. Stubbs, W. S u t h e r l a n d , A . B . Tomaney, T. V a n d e h e i a n d D . W e l c h

248

A G A P E : Results from Microlensing on Unresolved Stars Y, L e D u (for t h e A G A P E C o l l a b o r a t i o n )

253

Trajectories of the Images in Binary Microlensing V. Bozza

257

The O r i g i n of Microlensing Towards the L M C and H o w to Test It H . S. Z h a o

263

Session B3:

Next Generation Astronomical Searches

Pixel Lensing Towards Andromeda: the P O I N T - A G A P E Survey E . K e r i n s (for t h e P O I N T - A G A P E C o l l a b o r a t i o n )

269

SESSION C . N O N - B A R Y O N I C S E A R C H E S

Session C O :

Introduction to Non-Baryonk Dark Matter Searches

W I M P Searches with Cryogenic Detectors H. Kraus

275

Neutralino Dark Matter and Direct W I M P Searches S. Scope!

285

A N e w Model-Independent Method for Extracting Spin-Dependent Cross Section Limits from Dark Matter Searches D. R. Tovey, R. J . G a i t s k e t l , P . G o n d o l o , Y. Ramachers and L. Roszkowski

291

xi

Relic A x i o n s Radiated from A x i o n i c Strings M . Y a m a g u c k i ' , M . K a w a s a k i a n d J. Y o k o y a m a

297

A N e w Population o f W I M P s in the Solar System and Indirect Detection Rates L . B e r g s t r o m , T. D a m o u r , J , E d s j d ' , L . M . K r a u s s a n d P . U l l i o

305

Annihilations from the Galactic Centre G. B e r t o m , J . S i l k ' a n d G. S i g l

311

D a r k S U S Y — A Numerical Package for Dark Matter Calculations

318

in the M S S M P. G o n d o l o , J. Edsjd', L . B e r g s t r o m , P . U l l i o a n d E. A . Baltz Newtonian Dark Matter Identification and Search M . Ja. I v a n o v

324

Session C I : WPMP Detectors Results on the Investigation o f the W I M P Annual Modulation Signature with the s l O O K g Nal(TI) D A M A Set-up

331

R. B e r n a b e i , P . B e l l i , R. C e r u l l i , F . M o n t e c c h i a , M . A m a t o , G. I g n e s t i , A . I n c i c c h i t t i ' , D . P r o s p e r i , C. J . D a i , H . L H e , H . H . K u a n g a n d J. M . M a U K D M C Dark Matter Search with Inorganic Scintillators V. A . K u d r y a v t s e v , N . J . C. Spooner, P . K . L i g h t f o o t , J . W. R o b e r t s , M . J . L e h n e r , T. G a m b l e , T. B . L a w s o n , R. L u s c h e r , J . E . M c M i l l a n , B . M o r g a n , M . R o b i n s o n , D . R. Tovey, N . J . T. S m i t h , P . F . S m i t h ,

337

G. J . A l n e r , S. P . H a r t , J . D . L e w i n , R. M . P r e e c e , T. J . Sumner, W. G. Jones, J . J . Quenby, B . Ahmed, A . Bewick, D . Davidge, J . V. D a w s o n , A . S. H o w a r d , !. I v a n i o u c h e n k o v , M . K . J o s h i , V. Lebedenko, I . L i u b a r s k y a n d J . C. B a r t o n Search for W I M P s with the Large N a l ( T l ) Scintillator o f L L K G A N T V S. Y o s h i d a ' , H . E j i r i , K . F u s h i m i , K . H a y a s h i , T. K i s h i m o t o , M. K o m o r i , N . K u d o m i , K . Kume, H .K u r a m o t o , K . Matsuoka, H . O h s u m i , K . T a k a h i s a , Y. T s u j i m o t o a n d S. U m e h a r a

343

xii

L i m i t s on the W I M P - N u c l e o n Cross-Section from the Cryogenic Dark Matter Search R. J . G a i t s k e l l (for t h e C D M S C o l l a b o r a t i o n )

349

The Deployment of Z I P N o n - E q u i l i b r i u m Phonon Detectors i n C D M S II P. L . B r i n k f f o r t h e C D M S C o l l a b o r a t i o n )

355

Status Report on the R O S E B U D Dark Matter Experiment S. C e b r i d n , E . G a r c i a , D . Gonzalez, I . G. I r a s t o r z a , A . M o r a l e s , J . M o r a l e s , A . O r t i z de S o l d r z a n o , A . P e r u z z i . J- P i u m e d o n , M . L . Sarsa, S. Scopel, J . A . V i l l a r , N . C o r o n , G. D a m b i e r , J . L e b l a n c , P . de M a r c i l i a c ' a n d J . P . M o a l i c

361

Recent Results from the Canfranc Dark Matter Search with Germanium Detectors /. G. I r a s t o r z a , A . M o r a l e s , C. E . A a l s e t h , F . T. A v i g n o n e III, R. L . B r o d z i n s k i , S. C e b r i d n , E . G a r c i a , D . Gonzalez, W. K . H . S. M i l e y , J . M o r a l e s , A . O r t i z de S o l d r z a n o , J . P i u m e d o n , J . H . Reeves, M . L . Sarsa, S. Scopel a n d J. A . V i l l a r

367

Hensley,

Dark Matter Search in the E D E L W E I S S Experiment M. Chapellier, A . Benoit, L . Berge, A . Broniatowski, B. Chambon. G. L M. M. L. C.

373

C h a r d i n , P . C h a r v i n , M . D e Jesus, P . D i Stefano, D. Drain, D u m o u l i n , J . G a s c o n , G. G e r b i e r , C. G o i d b a c h , M . G o y o t , G r o s , J . P . H a d j o u t , S. H e r v e , A . J u i l l a r d , A . de Lesquen, L o i d l , J . M a l l e t , S. M a r n i e r o s , O. M a r t i n e a u , N . M i r a b o l f a t h i , M i r a m o n t i . L . M o s c a , X . - F . N a v i c k , G. N o l l e z , P . P a r i , P a s t o r , E . S i m o n , M . Stern a n d L . V a g n e r o n

Current Status o f the W I M P Search Using C a F Scintillator at O T O C o s m o Observatory 7". K i s h i m o t o , I . O g a w a , R. H a z a m a , S. A j i m u r a , K . M a t s u o k a , H . M i y a w a k i , S. S h i o m i , Y. T a n a k a , Y. I s h i k a w a , M . I t a m u r a , K . K i s h i m o t o , H . Sakai, D . Yokoyama, A , Katsuki, H. Ejiri, N. K n d o m i , K K u m e , H . O h s u m i a n d K. F u s h i m i

379

Status o f TeO, Detectors for W I M P s Searches A . A l e s s a n d r e l l o , C. B r o f f e r i o , O. C r e m o n e s i , E . F i o r i n i , A . N u c c i o t t i , M . P a v a n , G. Pessina, S. P i r r o , E . P r e v i t a l i ' , M . S i s t i , M . V a n z i n i , L Z a n o l t i , C. B u c c i , C. Pobes a n d A . G i u l i a n i

385

;

xiii

Dark Matter Search with L i t h i u m Fluoride at K a m i o k a K . M i u c h i ' , M . M i n o w a , A . T a k e d a , H . Sekiya, Y. S h i m i z u , Y. I n o u e , W. O o t a n i , Y. I t o , T. W a t a n a b e , S. M o r i y a m a a n d Y. O o t u k a

391

W I M P Searches with Superheated Droplet Detectors: Status and Prospects J . I . C o l l a r , D . L i m a g n e , T. M o r l a t , J . Puibasset, G. Waysand, T. A . G i r a r d a n d H . S. M i l e y

397

C R E S S T Dark Matter Search M . B r u c k m a y e r , C. C o z z i n i , P . d i Stefano, T. F r a n k , D . Hauff, F . P r o b s t , W. Seidel, I . Sergeyev, L . Stodolsky, F . v o n Feilitzsch, T. J a g e m a n n , J . J o c h u m , J . Schnagl, M . Stark, H . W u l a n d a r i , S. C o o p e r , R. K e e l i n g , H . K r a u s , J . M a r c h e s e , Y. Ramachers a n d C. B u c c i

403

Development o f Scintillating Calorimeters for the C R E S S T II Experiment P . d i Stefano', M . B r u c k m a y e r , C. C o z z i n i , T. F r a n k , D . Hauff, D . P e r g o l e s i , F . P r o b s t , W. Seidel, I . Sergeyev, L. Stodolsky, S. U c h a i k i n , S. C o o p e r , R. K e e l i n g , H . K r a u s , J . M a r c h e s e , Y. Ramachers, F . v o n F e i l i t z s c h , T. J a g e m a n n , J . J o c h u m , J . Schnagl, M . S t a r k , H . W u l a n d a r i a n d C. B u c c i

409

Recent Results from the H D M S Experiment H . V. K l a p d o r - K l e i n g r o t h a u s , L B a u d i s , A . D i e t z , G. Heusser, I . V. K r i v o s h e i n a , B . M a j o r o v i t s ' , St. K o l b a n d H . Strecker

415

A Superfluid ' H e Detector for Direct Dark Matter Search F . M a y e t , D . Santos, Yu. M . B u n k o v , G. D u h a m e l , H . G o d f r i n , F . N a r a g h i a n d G. P e r r i n

421

Status o f the P I C A S S O Project for Direct Dark Matter Search At B o u k h i r a , I . B o u s s a r o q u e , R. G o r n e a , M . D i M a r c o , L . L e s s a r d a n d V. Zacek'

427

Z E P L I N - I : A Single Phase L i q u i d X e Detector for Dark Matter Search /. I v a n i o u c h e n k o v ' , A . B e w i c k , W. G. Jones, I . Liubarsky, J . J . Quenby, T. J . Sumner, G. J . A l n e r , S. P . H a r t , J . D . L e w i n , R. M . P r e e c e , N . J . T. S m i t h a n d P . F . S m i t h

433

xiv

L X e D A M A Experiment: Results and Perspectives R. B e r n a b e i , P . B e l l i ' , R. C e r u l l i , F . M o n t e c c h i a , M . A m a t o , A . I n c i c c h i t t i , D . P r o s p e r i a n d C. J . D a i

438

Scintillation Characteristics for L o w Energy Recoils i n L i q u i d X e n o n .

446

Preliminary Results R. L u s c h e r , D . A k i m o v , A . B e w i c k , D . D a v i d g e , J . V, D a w s o n , A . S. H o w a r d , I . I v a n i o u c h e n k o v , W. G Jones, M . K. Joshi, V. A . K u d r y a v t s e v , T. B . L a w s o n , V. Lebendenko, M . J. Lehner, P . K . L i g h l f o o t , I . L i u b a r s k y , J . E . M c M i l l a n , C. D . Peak, J . J . Quenby, N . J . G Spooner, T. J . Sumner, D . R. Tovey a n d C. K . W a r d Z E P L I N - I I I : A Two-Phase X e n o n Dark Matter Detector T. J . Sumner (for t h e U K D M C , I T E P , C o l u m b i a , U C L A , Torino/CERN Collaboration)

452

Measurements with a Two-Phase X e n o n Prototype Dark Matter Detector A . S. H o w a r d ' , A . B e w i c k , D . C. R. D a v i d g e , J . V. D a w s o n , W. G. Jones, V. N . Lebedenko, T. J . Sumner, J.J. Quenby, D . Yu. A k i m o v , M . V. D a n i l o v , A , G. K o v a l e n k o a n d D . A . K o v a l e n k o

457

Session C2:

W I M P Detectors with Directional Sensitivity and Future Prospects

Neutron Recoils in the D R I F T Detector D . P . S n o w d e n - I f f t ' , T. O h n u k i , E . S. R y k o f f a n d

463 C. J . M a r t o f f

The Scintillation Efficiency o f Carbon and Hydrogen Recoils in an Organic L i q u i d Scintillator J . H o n g , W. W. C r a i g , P . G r a h a m , C. J . H a i l e y , N . J . C. a n d D . R. Tovey

Session C3:

475

Spooner

Axion Detectors

First R u n o f the P V L A S Experiment: Dark Matter Candidates Production and Detection G. C a n t a t o r e ' , F . d e l t a V a l l e , E . Z a v a t t i n i , F . B r a n d i , S. C a r u s o t t o , E . P o l l a c o , M . B r e g a n t , G. Ruoso, U. G a s t a l d i , R. P e n g o , G. d i D o m e n i c o , G. Z a v a t t i n i a n d E . M i l o t t i

481

XV

Status Report on the Large-Scale U . S . Search for H a l o A x i o n s E. J. D a w

487

Recent Results from the T o k y o A x i o n Helioscope Experiment Y. I n o u e , T. N a m b a , S. M o r i y a m a , M . M i n o w a , Y. T a k a s u , T. H o r i u c h i a n d A . Yamamoto

493

Session C4:

W I M P Detection by Indirect Techniques

W I M P Searches with A M A N D A - B I O J . E d s j d (for t h e A M A N D A C o l l a b o r a t i o n )

499

The A N T A R E S Neutrino Telescope: Status and Prospects S. L . C a r t w r i g h t (for t h e A N T A R E S C o l l a b o r a t i o n )

506

Detecting Dark Matter with G L A S T P. Ullio'

Session C5:

Neutrino Dark Matter Searches

Neutrinos and Extra Dimensions D . O. C a l d w e l l

513

Status o f T r i m a x i m a l Neutrino M i x i n g W. G. Scott

526

Palo Verde Results, K a m L A N D and C H O O Z G. G r a t i a * First S N O Results and Prospects D. Wark' M i n i B o o N e : Status and Prospects P . H . K a s p e r (for t h e M i n i B o o N e

532 Collaboration)

Preliminary Results and Status o f the M U N U Experiment C.

Broggini

538

xvi

Session C6:

Next Generation Neutrino, W I M P and Axion Techniques

C N G S Experimental Programme J. M a r t e a u

546

A Neutrino Factory

557

R. E d g e c o c k Detection of V e r y Small Neutrino Masses in Double-Beta Decay Using A. A. G.

570

Laser Tagging P i e p k e , P . V o g e l , P . P i c c h i , R. D e v o e , M . D a n i l o v , D o l g o l e n k o , O. Z e l d o v i c h , J . - L . V u i l l e u m i e r , F . P i e t r o p a o l o , G r a t i a , Y.-F. W a n g a n d G. G i a n n i n i

The Proposed O R L a N D Neutrino Facility F . T. A v i g n o n e I I I ' a n d Yu. V. E f r e m e n k o

578

Present Status and Future Plans o f the Boulby Underground Laboratory J . W. R o b e r t s ' , T. G a m b l e , V. A . K u d r y a v t s e v , M . J . L e h n e r , T. B . L a w s o n , P . K . L i g h t f o o t , R. L i i s c h e r , J . E . M c M i l l a n ,

590

B. G. P. A. V. J.

M o r g a n , M . R o b i n s o n , N . J . C. Spooner, D . R. Tovey, J . A l n e r , S. P . H a r t , J . D . L e w i n , R. M . P r e e c e , N . J . T. S m i t h , F . S m i t h , B . Ahmed, A . B e w i c k , D . D a v i d g e , J . V. D a w s o n , S. H o w a r d , I . I v a n i o u c h e n k o v , W. G. Jones, M .K . Joshi, Lebedenko, I . L i u b a r s k y , J . J . Quenby, T. J . Sumner and C. B a r t o n

G E N I U S and the Genius T F : A N e w Observatory for W I M P Dark Matter and Neutrinoless Double Beta Decay H . V. K l a p d o r - K l e i n g r o t h a u s a n d B . M a j o r o v i t s '

593

Prospects for a Large X e Detector T. J . Sumner

603

Towards One Tonne Direct W I M P Detectors: Have W e Got What It Takes? R- J . G a i t s k e l l

606

xvii

Session C 7 :

Implications for Astrophysical Neutrino Detection

Searching for Supernova Neutrino Bursts with O M N I S R. M a r s h a l l ' The S I R E N Solar Neutrino Experiment /, L i u b a r s k y ' , A . B e w i c k , T. J . Sumner, R. M a r s h a l l , I . M . B l a i r , J . A . E d g i n g t o n , N . J . T. S m i t h , P . F , S m i t h , S. L C a r t w r i g h t , P . K . L i g h t f o o t , V. A . K u d r y a v t s e v , J . E . M c M i l l a n a n d N . J . C. Spooner

618

Element-Loaded Organic Scintillators for Neutron and Neutrino Physics V. fi. B r u d a n i n , N . A . G u n d o r i n , D . V. F i l o s s o f o v , I . B . Nemtchenok', A . A . S m o l n i k o v , S. I . V a s i l i e v a n d V. I . B r e g a d z e

626

List of Participants

635

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SPACE, TIME, AND MATTER: COSMOLOGICAL P A R A M E T E R S 2001

Case

Western

LAWRENCE M . KRAUSS D e p a r t m e n t s of Physics and Astronomy Reserve University, 10900 Euclid Ave. Cleveland, O H 44106-7079

Over the past three years, our confidence in the inferred values of cosmological parameters has increased dramatically, confirming that the flat matter dominated Universe that dominated cosmological model building for the past 20 years does not correspond to the Universe in which we live. I review recent developments here and quote best fit current values for fundamental cosmological parameters. (Invited Review Lecture: Third International Conference on the Identification of Dark Matter, York, England, Sept 2000)

1

Introduction

The last decade has witnessed several r e m a r k a b l e transformations i n our knowledge o f the current state o f our universe, i n c l u d i n g the value of fund a m e n t a l c o s m o l o g i c a l parameters. T h e g o o d news is t h a t the a c t u a l values we seem to be c o n v e r g i n g o n are r i d i c u l o u s . T h u s , our increased e m p i r i c a l knowledge has gone h a n d i n h a n d w i t h increased t h e o r e t i c a l confusion. F o r theorists a n d observers alike, n o t h i n g c o u l d be more e x c i t i n g . In order to m a k e some a t t e m p t to have this review appear less b o r i n g t h a n it a c t u a l l y is, I have decided to g r o u p the cosmological parameters i n terms o f three general themes, h a r k i n g back to the famous book o f H e r m a n n W e y l , the t i t l e o f w h i c h nicely encompasses the business o f m o d e r n cosmology.

2 2.1

Space, T h e F i n a l Frontier Expansion

P r o b a b l y the m o s t i m p o r t a n t c h a r a c t e r i s t i c o f the space i n w h i c h we live is t h a t i t is e x p a n d i n g . T h e e x p a n s i o n rate, given by the H u b b l e C o n s t a n t , sets the o v e r a l l scale for m o s t other observables i n cosmology. T h u s it is o f v i t a l i m p o r t a n c e to p i n d o w n its value i f we hope t o seriously c o n s t r a i n other c o s m o l o g i c a l parameters.. F o r t u n a t e l y , over the past five years tremendous strides have been made in our e m p i r i c a l knowledge o f the H u b b l e constant. I briefly review recent developments a n d prospects for the future here.

1

2

H S T - K B Y Project T h i s is the largest scale endeavor c a r r i e d out over the past decade w i t h a goal o f a c h i e v i n g a 10 % absolute u n c e r t a i n t y i n the H u b b l e constant. T h e goal o f the project has been to use C e p h e i d l u m i n o s i t y distances t o 25 different galaxies located w i t h i n 25 Megaparsecs i n order to c a l i b r a t e a v a r i e t y of secondary distance i n d i c a t o r s , w h i c h i n t u r n c a n be used t o d e t e r m i n e the distance t o far further objects o f k n o w n redshift. T h i s i n p r i n c i p l e allows a measurement of the distance-redshift r e l a t i o n a n d t h u s the H u b b l e c o n s t a n t on scales where l o c a l peculiar velocities are insignificant. T h e four d i s t a n c e i n d i c a t o r s so constrained are: (1) the T u l l y F i s h e r r e l a t i o n , a p p r o p r i a t e for spirals, (2) the F u n d a m e n t a l plane, a p p r o p r i a t e for e l l i p t i c a l s , (3) surface brightness fluctuations, and (4) S u p e r n o v a T y p e l a distance measures. The H S T - K e y project has recently r e p o r t e d H u b b l e constant measurements for each of these methods, w h i c h I present below . W h i l e I s h a l l a d o p t these as q u o t e d , it is w o r t h p o i n t i n g out t h a t some c r i t i c s o f this a n a l y s i s have stressed t h a t this involves u t i l i z i n g d a t a o b t a i n e d by other g r o u p s , w h o themselves sometimes report different values o f the H u b b l e constant for the same d a t a sets. 1

F

H % /f£

= 71 ± 4 ± 7

p

= BF

H§> H % H

V a

A

N

78±8±10 = 69 ± 4 ± 6

l

a

= 68 ± 2 ± 5 i

1

=71±6kTn - Mpc~ (lo) S

In the weighted average quoted above, the d o m i n a n t c o n t r i b u t i o n t o the 9% one s i g m a error comes from an overall u n c e r t a i n t y i n the d i s t a n c e t o the L a r g e M a g e l l a n i c C l o u d . If the C e p h e i d M e t a l l i c i t y were shifted w i t h i n its allowed 4% u n c e r t a i n t y range, the best fit m e a n value for the H u b b l e C o n s t a n t from the H S T - K e y project w o u l d shift d o w n a r d t o 68 ± 6. S-Z

Effect:

The S u n y a e v - Z e l d o v i c h effect results from a shift i n the s p e c t r u m o f the C o s m i c M i c r o w a v e B a c k g r o u n d r a d i a t i o n due to s c a t t e r i n g o f the r a d i a t i o n b y electgrons as the r a d i a t i o n passes t h r o u g h i n t e r v e n i n g g a l a x y clusters o n the way t o our receivers on E a r t h . Because the e l e c t r o n t e m p e r a t u r e i n C l u s t e r s

3 exceeds t h a t i n the C M B , the r a d i a t i o n is s y s t e m a t i c a l l y shifted t o higher frequencies, p r o d u c i n g a deficit i n the i n t e n s i t y below some characteristic frequency, a n d a n excess above it. T h e a m p l i t u d e of the effect depends u p o n the T h o m p s o n s c a t t e r i n g scross section, a n d the electron density, i n t e g r a t e d over the p h o t o n ' s p a t h :

SZ A t the same t i m e the electrons i n the hot gas t h a t dominates the b a r y o n i c m a t t e r i n g a l a x y clusters also e m i t s X - R a y s , and the o v e r a l l X - R a y i n t e n s i t y is p r o p o r t i o n a l to the s q u a r e o f the electron density integrated a l o n g the line of sight t h r o u g h the cluster:

X - R a y U s i n g models of the cluster density profile one c a n t h e n use the the differing dependence o n n i n the two integrals above to e x t r a c t the p h y s i c a l p a t h - l e n g t h t h r o u g h the cluster. A s s u m i n g the r a d i a l extension of the cluster is a p p r o x i m a t e l y equal t o the extension across the line of sight one c a n compare the p h y s i c a l size o f the cluster t o the a n g u l a r size t o determine its distance. C l e a r l y , since this a s s u m p t i o n is o n l y g o o d i n a s t a t i s t i c a l sense, the use o f S - Z a n d X - R a y observations t o determine the H u b b l e constant cannot be done r e l i a b l y on the basis o f a single cluster observation, but r a t h e r on an ensemble. e

A recent p r e l i m i n a r y analysis o f several clusters

5Z

tf

= 60±10

0

2

yields:

k s ^ M p c —1

Type

l aS N (non-Key Project): O n e of the H S T K e y P r o j e c t distance estimators involves the use of T y p e l a S N as s t a n d a r d candles. A s p r e v i o u s l y e m p h a s i z e d , the K e y P r o j e c t does not p e r f o r m direct measurements o f T y p e l a supernovae b u t rather uses d a t a o b t a i n e d b y other gorpus. W h e n these groups perform a n independent a n a l ysis to derive a value for the H u b b l e constant they arrive at a smaller value t h a n t h a t q u o t e d b y the K e y P r o j e c t . T h e i r m o s t recent q u o t e d value is : 3

Xo

a

= 64te

l

ks~ Mpc-

1

4

A t the same t i m e , Sandage a n d collaborators have performed a n i n d e p e n 4

dent analysis o f S N e l a distances a n d o b t a i n :

if

l a 0

= 58 ± 6

l

k s ~ M p C

l

Surface B r i g h t n e s s F l u c t u a t i o n s a n d T h eG a l a x y D e n s i t y F i e l d : A n o t h e r recently used distance e s t i m a t o r involves the measurement o f fluctuations in the g a l a x y surface brightness, w h i c h c o r r e s p o n d t o density fluctuations a l l o w i n g a n estimate of the p h y s i c a l size o f a g a l a x y . T h i s measure yields a s l i g h t l y higher value for the H u b b l e constant : s

BF

H£

=

l

l

7i±4ks- Mpc~

Time Delays i n Gravitational Lensing: O n e o f the most remarkable observations associated w i t h observations of m u l t i p l e images of distant quasars due to g r a v i t a t i o n a l lensing i n t e r v e n i n g galaxies has been the measurement of the t i m e delay i n the t w o images o f quasar 0 0 9 5 7 + 561. T h i s time delay, measured quite a c c u r a t e l y t o be 417 ± 3 days is due to t w o factors: T h e path-length difference between the quasar a n d the earth for the light from the t w o different images, a n d the S h a p i r o g r a v i t a t i o n a l t i m e delay for the light rays t r a v e l i n g i n s l i g h t l y different g r a v i t a t i o n a l potential wells. If i t were n o t for t h i s second factor, a measurement o f the t i m e delay could be directly used to determine the distance o f the i n t e r v e n i n g galaxy. T h i s latter factor however, implies that a m o d e l of b o t h the galaxy, a n d the cluster i n w h i c h it is embedded must be used t o estimate the S h a p i r o t i m e delay. T h i s introduces a n a d d i t i o n a l model-dependent u n c e r t a i n t y i n t o the analysis. T w o different analyses y i e l d values : 6

H j

^

D

D

1

2

=89ii|(l-«)

ks-'Mpc-

1

= 7 4 ± g C l - ^

ks-'Mpc-

1

where K is a parameter w h i c h accounts for a possible d e v i a t i o n i n cluster parameters governing the overall induced g r a v i t a t i o n a l t i m e delay of the t w o signals from t h a t assumed i n the best fit. It is assumed i n the a n a l y s i s t h a t K is s m a l l .

b Summary: It is difficult to k n o w how t o best i n c o r p o r a t e a l l o f the q u o t e d estimates i n t o a single estimate, given their separate s y s t e m a t i c a n d s t a t i s t i c a l uncertainties. A s s u m i n g large n u m b e r statistics, where large here includes the nine quoted values, I p e r f o r m a s i m p l e weighted average o f the i n d i v i d u a l estimates, and find a n a p p r o x i m a t e average value;

v

1

1

Hf raW±3k - Mpc8

2.2

(1)

Geometry

It has r e m a i n e d a d r e a m o f o b s e r v a t i o n a l cosmologists to be able t o d i r e c t l y measure the geometry o f space-time rather t h a n infer the c u r v a t u r e o f the universe b y c o m p a r i n g the e x p a n s i o n rate to the m e a n mass density. W h i l e several such tests, based o n m e a s u r i n g g a l a x y counts as a f u n c t i o n of redshift, or the v a r i a t i o n of a n g u l a r diameter distance w i t h redshift, have been a t t e m p t e d i n the past, these have a l l been s t y m i e d b y the achilles heel of m a n y observational measurements i n cosmology, e v o l u t i o n a r y effects. Recently, however, measurements of the cosmic m i c r o w a v e b a c k g r o u n d have finally b r o u g h t us t o the t h r e s h o l d o f a d i r e c t measurement of geometry, independent of t r a d i t i o n a l a s t r o p h y s i c a l uncertainties. T h e idea b e h i n d this measurement is, i n p r i n c i p l e , quite s i m p l e . T h e C M B originates from a spherical shell located at the surface of last s c a t t e r i n g ( S L S ) , at a redshift of r o u g h l y Z fS 1000): If a fiducial l e n g t h c o u l d u n a m b i g o u s l y be d i s t i n g u i s h e d o n t h i s surface, then a d e t e r m i n a t i o n of the a n g u l a r size associated w i t h this l e n g t h w o u l d allow a d e t e r m i n a t i o n o f the i n t e r v e n i n g geometry: F o r t u n a t e l y , n a t u r e has p r o v i d e d such a fiducial length, w h i c h corresponds r o u g h l y t o the h o r i z o n size a t the t i m e the surface of last s c a t t e r i n g existed. T h e reason for this is also s t r a i g h t f o r w a r d . T h i s is the largest scale over w h i c h c a u s a l effects at the t i m e of the c r e a t i o n o f the surface of last s c a t t e r i n g c o u l d have left a n i m p r i n t . D e n s i t y fluctuations on such scales w o u l d result i n acoustic o s c i l l a t i o n s of the m a t t e r - r a d i a t i o n fluid, a n d the d o p p l e r m o t i o n o f electrons m o v i n g a l o n g w i t h this fluid w h i c h scatter o n photons e m e r g i n g from the S L S produces a c h a r a c t e r i s t i c peak i n the power s p e c t r u m o f fluctuations of the C M B R at a w a v e n u m b e r c o r r e s p o n d i n g to the a n g u l a r scale spanned b y this p h y s i c a l scale. These fluctuations s h o u l d also be v i s u a l l y d i s t i n g u i s h a b l e in a n i m a g e m a p o f the C M B , p r o v i d e d a resolution o n degree scales is possible. R e c e n t l y , t w o different ground-based b a l l o o n experiments, one l a u n c h e d in T e x a s a n d one launched i n A n t a r c t i c a have resulted i n maps w i t h the re-

6 COSMIC MICROWAVE

BACKGROUND

Figure I, A schematic diagram of the surface of last scattering, showing the distance traversed by C M B radiation.

7 , s

quired resolution . S h o w n below is a c o m p a r i s o n of the a c t u a l b o o m e r a n g m a p w i t h several s i m u l a t i o n s based on a gaussian r a n d o m s p e c t r u m o f density fluctuations i n a cold-dark m a t t e r universe, for o p e n , c l o s e d , a n d flat cosmologies. E v e n at this q u a l i t a t i v e level, i t is clear t h a t a flat universe p r o vides better agreement to between the s i m u l a t i o n s a n d the d a t a t h a n either an open or closed universe . ?

O n a more q u a n t i t a t i v e level, one c a n c o m p a r e the inferred p o w e r s p e c t r a w i t h predicted spectra . S u c h c o m p a r i s i o n s , for b o t h the B o o m e r a n g a n d M a x i m a results yields a constraint on the density p a r a m e t e r : 9

7

Angular Size of a Fixed Scale in Open, Closed, and Flat Universes: First Scale to Collapse after Recombination (^distance spanned by light ray ^horizon size)

dosed OPEN CLOSED —

FLAT

Figure 2. The geometry of the Universe and ray trajectories for C M B radiation.

fi = l . l ± . 1 2 ( 9 5 % C L )

(2)

For the first t i m e , it appears t h a t the l o n g s t a n d i n g prejudice of theorists, namely t h a t we l i v e i n a flat universe, may have been v i n d i c a t e d by observat i o n ! H o w e v e r , theorists c a n not be too self-satisfied by this result, because the source o f t h i s energy density appears t o be c o m p l e t e l y unexpected, a n d largely i n e x p l i c a b l e at the present t i m e , as we w i l l s h o r t l y see.

8

25°

Figure 3. Boomerang data visually compared to expectations for an open, closed, and flat C D M Universe.

3 3.1

Time Stellar

Ages

E v e r since K e l v i n and H e l m h o l t z first e s t i m a t e d the age o f the S u n t o be less t h a n 100 m i l l i o n years, a s s u m i n g t h a t g r a v i t a t i o n a l c o n t r a c t i o n was its p r i m e energy source, there has been a tension between stellar age estimates a n d estimates o f the age of the universe In the case of the K e l v i n - H e l m h o l t z case, the age o f the s u n appeared too short to a c c o m o d a t e a n E a r t h w h i c h was several b i l l i o n years o l d . O v e r m u c h of the latter half of the 2 0 t h c e n t u r y , the opposite p r o b l e m d o m i n a t e d the cosmological landscape. S t e l l a r ages, based o n nuclear reactions as measured i n the l a b o r a t o r y , a p p e a r e d t o be t o o o l d to a c c o m o d a t e even an o p e n universe, based on estimates o f the H u b b l e p a -

9 rameter. A g a i n , as I s h a l l o u t l i n e i n the next section, the observed e x p a n s i o n rate gives a n u p p e r l i m i t on the age of the U n i v e r s e w h i c h depends u p o n the e q u a t i o n o f state, a n d the overall energy density of the d o m i n a n t m a t t e r i n the U n i v e r s e . T h e r e are several methods to a t t e m p t to determine stellar ages, b u t I w i l l concentrate here o n m a i n sequence fitting t e c h n i q u e s , because those are the ones I have been i n v o l v e d i n . T h e basic i d e a b e h i n d m a i n sequence fitting is simple. A stellar m o d e l is constructed b y s o l v i n g the basic equations of stellar structure, i n c l u d i n g conservation o f mass a n d energy a n d the a s s u m p t i o n o f h y d r o s t a t i c e q u i l i b r i u m , and the equations o f energy t r a n s p o r t . B o u n d a r y c o n d i t i o n s at the center of the star a n d at the surface are t h e n used, a n d c o m b i n e d w i t h assumed equation of s t a t e equations, opacities, a n d nuclear r e a c t i o n rates i n order to evolve a star o f given mass, and elemental c o m p o s i t i o n . 5

G l o b u l a r clusters are c o m p a c t stellar systems c o n t a i n i n g u p to 1 0 stars, w i t h l o w heavy element abundance. M a n y are located i n a s p h e r i c a l halo a r o u n d the g a l a c t i c center, suggesting they formed early i n the h i s t o r y o f our g a l a x y . B y m a k i n g a cut on those clusters w i t h large halo velocities, and lowest m e t a l l i c i t i e s (less t h a n l / 1 0 0 t h the solar value), one a t t e m p t s to observation ally d i s t i n g u i s h the oldest such systems. Because these systems are c o m p a c t , one c a n safely assume t h a t a l l the stars w i t h i n t h e m formed at a p p r o x i m a t e l y the same t i m e . Observers measure the color a n d l u m i n o s i t y o f stars i n such clusters, p r o d u c i n g c o l o r - m a g n i t u d e d i a g r a m s o f the t y p e shown i n F i g u r e 2 (based o n d a t a from . 1 0

N e x t , u s i n g stellar models, one c a n a t t e m p t t o evolve stars o f differing mass for the m e t a l l i c i t i e s a p p r o p r i a t e t o a given cluster, i n order to fit o b servations. A p o i n t w h i c h is often conveniently chosen is the so-called m a i n sequence-turnoff ( M S T O ) p o i n t , the p o i n t i n w h i c h h y d r o g e n b u r n i n g ( m a i n sequence) stars have e x h a u s t e d t h e i r s u p p l y of h y d r o g e n i n the core. After the M S T O , the stars q u i c k l y e x p a n d , become brighter, a n d are referred to as R e d G i a n t B r a n c h ( R G B ) stars. H i g h e r mass stars develop a h e l i u m core t h a t is so hot a n d dense t h a t h e l i u m fusion begins. These form along the h o r i z o n t a l b r a n c h . Some stars a l o n g this b r a n c h are unstable to r a d i a l pulsations, the so-called R R L y r a e stars m e n t i o n e d earlier, w h i c h are i m p o r t a n t distance i n d i c a t o r s . W h i l e one i n p r i n c i p l e c o u l d a t t e m p t to fit theoretical isochrones (the l o c u s of points o n the p r e d i c t e d C M curve c o r r e s p o n d i n g to different mass stars w h i c h have evolved to a specified age), t o observations at any p o i n t , the m a i n sequence t u r n o f f is b o t h sensitive t o age, a n d involves m i n i m a l ( t h o u g h j u s t h o w m i n i m a l r e m a i n s to be seen) theoretical uncertainties.

10

Figure 4. Color-magnitude diagram for a typical globular cluster, M15. Vertical axis plots the magnitude (luminosity) of the stars in the V wavelength region and the horizontal axis plots the color (surface temperature) of the stars.

D i m e n s i o n a l analysis tells us that the m a i n sequence t u r n o f f s h o u l d be a sensitive function of age. T h e l u m i n o s i t y o f m a i n sequence stars is v e r y roughly p r o p o r t i o n a l to the t h i r d power of solar mass. H e n c e the t i m e i t takes to b u r n the hydrogen fuel is p r o p o r t i o n a l to the t o t a l a m o u n t o f fuel ( p r o p o r t i o n a l to the mass M ) , d i v i d e d by the L u m i n o s i t y — p r o p o r t i o n a l t o M . Hence the lifetime of stars o n the m a i n sequence is r o u g h l y p r o p o r t i o n a l to the inverse square of the stellar mass. 3

O f course the a b i l i t y to go b e y o n d this rough a p p r o x i m a t i o n depends c o m pletely on the on the confidence one has i n one's stellar models. It is w o r t h n o t i n g t h a t several improvements i n stellar m o d e l i n g have recently c o m b i n e d to lower the o v e r a l l age estimates of g l o b u l a r clusters. T h e i n c l u s i o n of diffusion lowers the age of g l o b u l a r clusters by a b o u t 7% , a n d a recently i m p r o v e d equation o f state w h i c h incorporates the effect o f C o u l o m b interactions has lead to a further 7% r e d u c t i o n i n overall ages. O f course, w h a t is most i m p o r t a n t for the c o m p a r i s o n o f c o s m o l o g i c a l predictions w i t h inferred age estimates is the uncertainties i n these a n d other stellar m o d e l p a r a m e t e r s , and not merely their best fit values. 1 1

1 2

O v e r the course of the past several years, I a n d m y c o l l a b o r a t o r s have

11

t r i e d t o i n c o r p o r a t e stellar m o d e l uncertainties, a l o n g w i t h o b s e r v a t i o n a l u n certainties i n t o a self consistent M o n t e C a r l o analysis w h i c h m i g h t a l l o w one to e s t i m a t e a r e l i a b l e range o f g l o b u l a r cluster ages. O t h e r s have c a r r i e d out independent, b u t s i m i l a r studies, a n d at the present t i m e , r o u g h agreement has been o b t a i n e d between the different groups (i.e. s e e ) . 13

I w i l l n o t b e l a b o r the d e t a i l e d h i s t o r y o f a l l such efforts here. T h e most c r u c i a l i n s i g h t has been t h a t stellar m o d e l uncertainties are small i n c o m parison to a n overall o b s e r v a t i o n a l u n c e r t a i n t y inherent i n fitting p r e d i c t e d m a i n sequence l u m i n o s i t i e s to observed turnoff m a g n i t u d e s . T h i s m a t c h i n g depends c r u c i a l l y on a d e t e r m i n a t i o n o f the distance t o g l o b u l a r clusters. T h e u n c e r t a i n t y i n this distance scale produces b y far the largest u n c e r t a i n t y i n the q u o t e d age estimates. I n m a n y studies, terms of the inferred tude c a n , i n t u r n , be M„(RR)of R R Lyrae

the distance to g l o b u l a r clusters c a n be p a r a m e t r i z e d i n m a g n i t u d e of the h o r i z o n t a l b r a n c h stars. T h i s m a g n i presented i n terms of the inferred absolute m a g n i t u d e , v a r i a b l e stars l o c a t e d on the h o r i z o n t a l b r a n c h .

I n 1997, the H i p p a r c o s satellite p r o d u c e d its catalogue o f p a r a l l a x e s of nearby stars, c a u s i n g an apparent r e v i s i o n i n distance estimates. T h e H i p p a r cos p a r a l l a x e s seemed t o be s y s t e m a t i c a l l y smaller, for the smallest m e a s u r e d parallaxes, t h a n p r e v i o u s t e r r e s t r i a l l y d e t e r m i n e d p a r a l l a x e s . C o u l d this represent the u n a n t i c i p a t e d s y s t e m a t i c u n c e r t a i n t y t h a t D a v i d has suspected? Since a l l the d e t a i l e d analyses h a d been p r e - H i p p a r c o s , several groups s c r a m bled to i n c o r p o r a t e the H i p p a r c o s catalogue i n t o their analyses. T h e i m m e d i ate result was a generally lower m e a n age estimate, r e d u c i n g the m e a n value to 11.5-12 G y r , a n d a l l o w i n g ages of the oldest g l o b u l a r clusters as low as 9.5 G y r . H o w e v e r , w h a t is also clear is t h a t there is now an e x p l i c i t s y s t e m a t i c u n c e r t a i n t y i n the R R L y r a e distance m o d u l u s w h i c h dominates the results. Different measurements are no longer consistent. D e p e n d i n g u p o n w h i c h distance e s t i m a t o r is correct, a n d there is now better evidence t h a t the distance estimators w h i c h disagree w i t h H i p p a r c o s - b a s e d m a i n sequence fitting s h o u l d not be d i s m i s s e d o u t of h a n d , the best-fit g l o b u l a r cluster estimate c o u l d shift up perhaps l a , or a b o u t 1.5 G y r , t o about 13 G y r . W i t h i n the p a s t two years, B r i a n C h a b o y e r a n d I have r e a n a l y z e d globular cluster ages, i n c o r p o r a t i n g new nuclear r e a c t i o n rates, cosmological estimates of the H e a b u n d a n c e , a n d most i m p o r t a n t l y , several new estimates of M „ ( R I X ) . T h e result is t h a t while s y s t e m a t i c uncertainties clearly s t i l l d o m i nate, we argue t h a t the m e a n age of the oldest g l o b u l a r clusters has increased a b o u t 1 G y r , to be 1 2 . 7 . | (95%) G y r , w i t h a 95 % confidence range o f a b o u t 11-16 G y r . It is t h i s range t h a t I shall now c o m p a r e to t h a t d e t e r m i n e d u s i n g the H u b b l e estimates given earlier. 4

h

?

12 3.2

H u b b l e Age

A s a l l u d e d to earlier, i n a F r i e d m a n - R o b e r t s o n - W a l k e r U n i v e r s e , the age o f the U n i v e r s e is d i r e c t l y related to b o t h the overall density o f energy, a n d to the equation of state o f the d o m i n a n t component of this energy density. The equation o f state is p a r a m e t e r i z e d by the r a t i o to — p / p , where p stands for pressure a n d p for energy density. It is this ratio w h i c h enters i n t o the second order F r i e d m a n equation d e s c r i b i n g the change i n H u b b l e p a r a m e t e r w i t h t i m e , w h i c h i n t u r n determines the age o f the U n i v e r s e for a specific net t o t a l energy density. T h e fact t h a t this depends on two independent parameters has meant t h a t one could reconcile possible conflicts w i t h g l o b u l a r cluster age estimates b y a l t e r i n g either the energy density, or the equation o f state. A n o p e n u n i v e r s e , for e x a m p l e , is older for a given H u b b l e C o n s t a n t , t h a n is a flat u n i v e r s e , w h i l e a flat universe d o m i n a t e d b y a cosmological constant can be o l d e r t h a n an open m a t t e r d o m i n a t e d universe. If, however, we i n c o r p o r a t e the recent geometric d e t e r m i n a t i o n w h i c h suggests we live i n a flat U n i v e r s e i n t o our analysis, t h e n our c o n s t r a i n t s o n the possible equation of state on the d o m i n a n t energy density of the universe become more severe. If, for existence, we allow for a diffuse c o m p o n e n t t o the t o t a l energy density w i t h the equation of state o f a c o s m o l o g i c a l constant (LJ — —1), t h e n the age of the U n i v e r s e for various c o m b i n a t i o n s of m a t t e r a n d cosmological constant are s h o w n below.

Table 1. Hubble Ages for a Flat Universe, H

0

1 0.2 0.3 0.35

n» 0 0.8 0.7 0.65

= 68 ± 6, ("2o")

to 9.7 ± 1 15.3 ± 1 . 5 13.7 ± 1 . 4 12.9 ± 1.3

C l e a r l y , a m a t t e r - d o m i n a t e d fiat universe is i n t r o u b l e i f one w a n t s t o reconcile the inferred H u b b l e age w i t h the lower l i m i t on the age of t h e universe inferred from g l o b u l a r clusters. I n fact, i f one t o o k the above c o n s t r a i n t s a t face value, such a U n i v e r s e i s r u l e d o u t o n t h e basis of age estimates a n d the H u b b l e c o n s t a n t estimates. However, I a m o l d e n o u g h to k n o w t h a t s y s t e m a t i c uncertainties i n cosmology often shift parameters well outside t h e i r f o r m a l two s i g m a , or even three s i g m a l i m i t s . In order t o definitely rule out a flat m a t t e r d o m i n a t e d universe using a c o m p a r i s o n of stellar a n d H u b b l e ages,

13

uncertainties i n b o t h w o u l d have t o be reduced b y at least a factor o f two. 4

Matter

H a v i n g i n d i r e c t l y p r o b e d the nature of m a t t e r i n the U n i v e r s e u s i n g the previous estimates, it is now t i m e to t u r n to direct constraints t h a t have been derived i n the past decade. Here, perhaps more t h a n any other area of observ a t i o n a l cosmology, new observations have changed the way we t h i n k a b o u t the U n i v e r s e . 4-1

The B a r y o n D e n s i t y :

a re-occuring crisis?

The success of B i g B a n g Nucleosynthesis i n p r e d i c t i n g i n the cosmic a b u n dances o f the light elements has been m u c h heralded. Nevertheless, the finer the a b i l i t y to e m p i r i c a l l y infer the p r i m o r d i a l abundances on the basis of observations, the greater the a b i l i t y to uncover some s m a l l d e v i a t i o n from the predictions. O v e r the past five years, two different sets o f observations have threatened, a t least i n some people's m i n d s , to o v e r t u r n the simplest B B N model p r e d i c t i o n s . I believe it is fair t o say t h a t most people have accepted that the first t h r e a t was o v e r b l o w n . T h e concerns about the second have yet to fully subside. i. P r i m o r d i a l D e u t e r i u m : T h e p r o d u c t i o n of p r i m o r d i a l d e u t e r i u m d u r ing B B N is a m o n o t o n i c a l l y decreasing f u n c t i o n of the b a r y o n density s i m p l y because t h e greater this density the more efficiently protons a n d neutrons get processed t o h e l i u m , a n d d e u t e r i u m , as a n i n t e r m e d i a r y i n this reactions set, is thus also m o r e efficiently processed at the same t i m e . T h e p r o b l e m w i t h inferring the p r i m o r d i a l d e u t e r i u m abundance by using present day measurements of d e u t e r i u m abundances i n the solar s y s t e m , for e x a m p l e , is t h a t d e u t e r i u m is highly processed (i.e. destroyed) i n stars, a n d no one has a g o o d enough model for galactic c h e m i c a l e v o l u t i o n to w o r k backwards from the observed abundances i n order to adequately c o n s t r a i n d e u t e r i u m at a level where this constraint c o u l d significantly test B B N estimates. T h r e e years ago, the s i t u a t i o n regarding d e u t e r i u m as a probe o f B B N changed d r a m a t i c a l l y , w h e n D a v i d T y t l e r and Scott B u r i e s c o n v i n c i n g l y measured the d e u t e r i u m f r a c t i o n i n h i g h redshift hydrogen clouds t h a t absorb light from even higher redshift quasars. Because these clouds are at h i g h redshift, before significant star f o r m a t i o n has o c c u r r e d , l i t t l e post B B N d e u t e r i u m processing is t h o u g h t t o have taken place, and thus the measured value gives a reasonable h a n d l e on the p r i m o r d i a l B B N abundance. T h e best measured system y i e l d s a d e u t e r i u m t o h y d r o g e n fraction o f 1 4

14

(D/H)

= (3-3. ± 0.5) x 1 0

- 5

(3)

(2 3.

to o b t a i n H

0

= 64 ± 6 k m / s / M p c .

Several groups have brought theoretical models to bear o n the d e t e r m i n a tion o f the H u b b l e constant using T y p e la supernovae. Hoflich a n d K h o k h l o v (1996) c o m p a r e d 26 supernovae w i t h m o d e l light curves and found H = 67 ± 9 k m / s / M p c . B r a n c h (1998) suggests this s h o u l d be revised t o 56 ± 5. T h e same two authors found H = 55 i f they i n c l u d e d a theoretical version of the M B - A M r e l a t i o n . Nugent et al (1995) fitted n o n - L T E m o d e l spectra to observations a n d found H = 60 + 14,-11. In a recent analysis T r i p p and B r a n c h (1999) conclude that the best estimate for the H u b b l e constant from T y p e l a supernovae was H „ = 62 ± 5 k m / s / M p c . G r a v i t a t i o n a l lens t i m e delay: P

0

1

5

0

A n analysis by F a l c o et al (1997) o f the g r a v i t a t i o n a l lens t i m e delay s y s t e m 0957+561 gave H = 62 ± 7 k m / s / M p c . K o o p m a n s and Fassnacht (1999) use 5 g r a v i t a t i o n a l lenses to determine H „ = 64 ± 1 1 k m / s / M p c S u n y a e v - Z e l d o v i c h effect: Recent work on S Z clusters includes M y e r s et a l (1997), B i r k i n s h a w (1999) a n d Reese et a l (2000). B i r k i n s h a w et al (2000) has given H — 54 ± 8 ± 10 k m / s / M p c for 9 clusters. 0

0

T o s u m m a r i z e , m y estimate for H

G


9.5 G y r [62]), radioactive dating of stars v i a the thorium and europium abundances (15.2 ± 3.7 G y r [63]), and studies of globular clusters (10-15 G y r , depending on whether H i p p a r c o s parallaxes of Cepheids are adopted [64,65]). Evidently, there is no longer a problem that the age of the oldest stars seems greater than the dynamical age of the Universe.

40

D I S C U S S I O N H i g h - r e d s h i f t SNe l a a r e o b s e r v e d t o be d i m m e r t h a n expected i n a n empty Universe ( i . e . , ( i u = 0 ) w i t h no c o s m o l o g i c a l c o n s t a n t . A cosmological explanation for this observation is that a positive vacuum energy density accelerates the expansion. Mass density i n the Universe exacerbates this problem, requiring even more vacuum energy. For a Universe with [J^/ == 0.2, the average M L C S distance m o d u l i of the well-observed SNe are 0.25 mag larger (i.e., 12.5% greater distances) than the prediction from i l = 0. The average M L C S distance moduli are still 0.18 mag bigger than required for a 68.3% {Iff} consistency i n a universe w i t h £l = 0.2 and without a cosmological constant. T h e derived value of go is —0.75 ± 0.32, i m p l y i n g that the expansion of the Universe is accelerating. If S1A really is constant, then at least the region of the Universe we have observed (z £ 0.8) w i l l expand eternally. Under the simplifying assumption of global homogeneity and isotropy, the entire Universe w i l l behave i n this manner. A very important point is that the dispersion i n the peak luminosities of S N e l a ( 0 would weaken. Conversely, if the distant, explosions are more powerful, then the case for acceleration strengthens. Theorists are not yet sure what the sign of the effect w i l l be, if it's present at all; different assumptions lead to different conclusions [66-70]. A

Of course, it is very difficult to obtain an independent measure of the peak luminosity of high-z SNe la, and hence to directly test for luminosity evolution. However, we can more easily determine whether o t h e r observable properties of lowz and high-z SNe l a differ. If they are all the same, it is more probable that, the peak luminosity is constant as well — but if they differ, then the peak luminosity might also bo affected (e.g., [66]). Drell et a l . [71], for example, argue that- there are

41

reasons to suspect evolution, because the average properties of existing samples of high-z and low-z S N e l a seem to differ (e.g., the high-z SNe l a are more uniform). T h e local sample of S N e l a displays a weak correlation between light-curve shape (or luminosity) and host galaxy type, i n the sense that the most luminous SNe l a w i t h the broadest light curves only occur i n late-type galaxies. B o t h early-type and late-type galaxies provide hosts for dimmer SNe l a with narrower light curves [31]. T h e mean luminosity difference for SNe l a i n late-type and early-type galaxies is n> 0.3 mag. In addition, the S N l a rate per unit luminosity is almost twice as high i n late-type galaxies as i n early-type galaxies at the present epoch [72]. These results may indicate an evolution of SNe l a w i t h progenitor age. Possibly relevant physical parameters are the mass, metallicity, and C / O ratio of the progenitor [66]. We expect that the relation between light-curve shape and luminosity that applies to the range of stellar populations and progenitor ages encountered i n the late-type and early-type hosts i n our nearby sample should also be applicable to the range we encounter i n our distant sample. In fact, the range of age for S N l a progenitors in the nearby sample is likely to be l a r g e r than the change i n mean progenitor age over the 4-6 G y r lookback time to the high-z sample. Thus, to first order at least, our local sample should correct our distances for progenitor or age effects. We can place empirical constraints on the effect that a change i n the progenitor age would have on our S N l a distances by comparing subsamples of low-redshift SNe l a believed to arise from old and young progenitors. In the nearby sample, the mean difference between the distances for the early-type (8 SNe la) and late-type hosts (19 SNe la), at a given redshift, is 0.04 ± 0.07 mag from the M L C S method. This difference is consistent w i t h zero. Even if the S N l a progenitors evolved from one population at low redshift to the other at high redshift, we still would not explain the surplus i n mean distance of 0.25 mag over the C l \ = 0 prediction. Moreover, it is reassuring that initial comparisons of high-redshift S N l a spectra appear remarkably similar to those observed at low redshift. For example, the spectral characteristics of S N 1998ai (z = 0.49) appear to be essentially indistinguishable from those of normal low-redshift SNe l a ; see Figure 7. In fact, the most obviously discrepant spectrum i n this figure is the second one from the top, that of S N 1994B ( z — 0.09); it is intentionally included as a "decoy" that illustrates the degree to which even the spectra of nearby, relatively normal SNe l a can vary. Nevertheless, it is important to note that a dispersion in luminosity (perhaps 0.2 mag) exists even among the other, more normal SNe l a shown i n Figure 7; thus, our spectra of S N 1998ai and other high-redshift S N e l a are not yet sufficiently good for independent, p r e c i s e determinations of luminosity from spectral features [73]. M a n y of them, however, are sufficient for ruling out other supernovae types (Figure 8), or for identifying gross peculiarities such as those shown by SNe 1991T and 1991bg; see C o i l e t a l . [74]. We can help verify that the SNe at ! « 0.5 being used for cosmology do not belong to a subluminous population of SNe l a by examining restframe / - b a n d light curves. N o r m a l , nearby SNe l a show a pronounced second m a x i m u m i n the / band about a m o n t h after the first m a x i m u m and typically about 0.5 mag fainter (e.g.,

42

[75,18]). Subluminous SNe la, i n contrast, do not show this second m a x i m u m , but rather follow a linear decline or show a muted second m a x i m u m [15]. A s discussed by Riess et a l . [76], some evidence for the second m a x i m u m is seen from our existing ./-band (restframe /-band) data on S N 1999Q { z = 0.46); see Figure 9. However, better data on more SNe l a are needed to confirm the effect.

iiOO

4000

4500 5000 5500 6000 Kcsl Wavelength (Angsliams)

6500

3000

4000 5000 Resl WDvelHnqth (A)

6000

F i g u r e 7 (left): Spectral comparison (in f x ) of S N 1998ai (2 = 0.49; K e c k spectrum) with low-redshift (z < 0.1) SNe l a at a similar age (~- 5 days before m a x i m u m brightness), from [48j. T h e spectra of the low-redshift S N e l a were resampled and convolved with Gaussian noise to match the quality of the spectrum of S N 1998ai. Overall, the agreement i n the spectra is excellent, tentatively suggesting that distant SNe l a are physically similar to nearby S N e l a . S N 1994B (z = 0.09) differs the most from the others, and was included as a "decoy." F i g u r e 8 ( r i g h t ) : Heavily smoothed spectra of two high-z SNe ( S N 1999ff at z = 0.455 and S N 1999fv at z — 1.19; quite noisy below —3500 A ) are presented along w i t h several low-z S N l a spectra (SNe 1989B, 1992A, and 1981B), a S N l b spectrum (SN 1993J), and a S N Ic spectrum ( S N 19941); see [1] for a discussion of spectra of various types of SNe. T h e date of the spectra relative to B - b a n d m a x i m u m is shown in parentheses after each object's name. Specific features seen i n S N 1999ff and labeled with a letter are discussed by C o i l et a l . [74]. T h i s comparison shows that the two high-z SNe are most likely SNe l a . Another way of using light curves to test for possible evolution of S N e l a is to see whether the rise time (from explosion to m a x i m u m brightness) is the same for high-z and low-z SNe l a ; a difference might indicate that the peak luminosities are

43

also different [66]. We recently measured the risetime of nearby SNe l a , using d a t a from K A I T , the Beijing A s t r o n o m i c a l Observatory ( B A O ) S N search, and a few amateur astronomers [77]. T h o u g h the exact value of the risetime is a function of peak luminosity, for typical low-z SNe l a we find 20.0 ± 0.2 days. We pointed out [78] that this differs by 5.8cr from the preliminary risetime of 17.5 ± 0.4 days reported i n conferences by the S C P [79-81]. However, a more thorough analysis of the S C P d a t a [82] shows that the high-z uncertainty of ± 0 . 4 days that the S C P originally reported was m u c h too small because it d i d not account for systematic effects. The revised discrepancy w i t h the low-2 risetime is about 2 0. B

But even the dust postulated by Aguirre [84,87,88] is not c o m p l e t e l y gray, having a size of about 0.1 (im. We can test for such nearly gray dust by observing highredshift SNe l a over a wide wavelength range to measure the color excess it would introduce. If A = 0.25 mag, then E { U - 1 ) and E ( B - I ) should be 0.12-0.16 mag [84,87]. If, on the other hand, the 0.25 mag faintness is due to A , then no such reddening should be seen. T h i s effect is measurable using proven techniques; so far, with just one S N l a ( S N 1999Q; Figure 10), our results favor the no-dust hypothesis v

45

to better than 2 a [76], but more work along these lines is certainly warranted. Suppose, though, that for some reason the dust is v e r y gray, or our color measurements are not sufficiently precise to rule out Aguirre's (or other) dust. If the cumulative amount of gray dust along the line of sight grows linearly w i t h increasing redshift, we expect that the deviation of the S N l a peak apparent magnitude from the low-flftfi zero-A model (Figure 3) will continue growing, to first order (Figure 11), If, on the other hand, the observed faintness of high-z SNe l a is a consequence of positive A , the deviation should actually begin to decrease at z s= 0.8 (Figure 11). In essence, we are looking so far back i n time that the A effect becomes small compared w i t h n ; the Universe is decelerating at that epoch. Thus, we are embarking on a campaign to find and monitor z = 0.8-1.2 SNe l a . Given the expected uncertainties (Figure 11), a sample of 10-20 SNe l a should give a good statistical result. Note that this test also applies to other systematic effects that grow monotonically w i t h redshift, as may be expected of possible evolution of the white dwarf progenitors (e.g., [66,67]), or gravitational lensing [89]. Indeed, this is our most decisive test to distinguish between A and systematic effects. Unless evolution of dust, or of the progenitors, or of the lenses is fixed i n such a way as to mimic the effects of A (e.g., [71]), our claim of f2 > 0 will become much more convincing if the deviation of apparent magnitude decreases in the expected manner. Such a turnover (Figure 11) can be considered the "smoking gun" of A . M

A

Redshift

F i g u r e 1 1 : T h e H Z T S N l a data from Figure 3 ( o p e n c i r c l e s ) are plotted relative to an empty universe ( h o r i z o n t a l l i n e ) . The two faint curves are the best-fitting A model, and the Sljw = 1 (SIA — 0) model. T h e darker curve shows a systematic bias that increases linearly w i t h z and is consistent w i t h our z — 0.5 data. T h e expected observational uncertainties of hypothetical SNe l a at redshifts of 0.85 and 1.2 are shown (filled circles).

46

CONCLUSIONS T h e luminosity distances of the high-redshift T y p e l a supernovae studied by the High-z Supernova Search Team exceed the prediction of a low mass-density ( f i ;a 0.2) universe by about 0.25 mag. A cosmological explanation is provided by a positive cosmological constant at roughly the Z u confidence level, w i t h the prior belief that S 1 > 0. We also find that the expansion of the Universe is currently accelerating ( q < 0, where q = £IM/2 ~ ^A)independent results of the Supernova Cosmology Project are fully consistent w i t h these conclusions. Moreover, recent precise measurements of the cosmic microwave background radiation strongly suggest that the Universe is flat (iltotai = f ^ M + ^ A = 1); hence, if CIM ~ 0,3 (as suggested by many studies, such as of clusters of galaxies), then about 70% of the energy density of the Universe must consist of vacuum energy whose precise nature and evolution are unknown (but definitely not radiation, n o r m a l matter, or dark matter). Using the best current values of the Hubble constant, J 1 , and U A , we find that the dynamical age of the Universe is 14.2 ± 1 . 7 G y r , i n c l u d i n g systematic uncertainties i n the Cepheid distance scale used for the host galaxies of three nearby SNe l a . T h i s value is comparable to the derived ages of globular star clusters. M

M

T

a

n

e

0

M

Though the consistent results from the microwave background experiments are reassuring, we are i n the process of testing as exhaustively as possible a l l systematic biases that could be affecting the S N l a results. For example, qualitative comparisons of spectra of low-z and high-z SNe l a do not reveal obvious differences, and quantitative tests are i n progress. Moreover, the restframe / - b a n d light curves of low-z SNe l a and a single measured high-z S N l a look similar, as do their broadband colors. T h e risetimes of low-z and high-z SNe l a may differ a l i t t l e , but the statistical significance of this result is not high, and i n any case the early part of the light curve may have little bearing on the peak luminosity. Further tests are in progress. Compelling evidence for acceleration may come i n the next few years from a comparison of the peak apparent brightness of z > 0.8 SNe l a w i t h the predictions of various models; the signature of nonzero A is quite distinct from that of dust, S N evolution, or other effects that grown w i t h redshift.

ACKNOWLEDGMENTS We thank all of our collaborators i n the H Z T for their contributions to this work. A . V . F . ' s supernova research at U . C . Berkeley is supported by N S F grants A S T 9417213 and AST-9987438, and by grants GO-7505 and GO-S177 from the Space Telescope Science Institute, which is operated by the Association of Universities for Research i n Astronomy, Inc., under N A S A contract N A S 5-26555. A . V . F . is grateful to the meeting organizers for travel funds.

4/

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D Y N A M I C A L

R E C O V E R Y

O F C O S M O L O G I C A L

C O N S T A N T

S. C A P O Z Z I E L L O A N D G . L A M B I A S E D i p a r t i m e n t o d i Science Fistcke E . R .Caianiello, U m v e r s i t a di S a l e r n o , 1-84081 Baronissi, Salerno, Italy. I s t i t u t o N a z i o n a l e di F i s i c a N u c l e a r e , sezione di Napoli. E-mail: capozzielto,[email protected] We discuss the meaning of ;i lime dependent "cosmological constant" and give a set of conditions to recover asymptotic de Sitter behaviour for a ciass of cosmological models in the framework of extended gravity theories. To this purpose we introduce a time-dependent (effective) quantity which asymptotically becomes the true cosmological constant. We deal with scalar-tensor theories. Furthermore the existence of the cosmological constant can be connected to a nonminima! derivative coupling, in the action of gravity, between the geometry and the kinetic part of a given scalar field without introducing any effective potential of scalar fields.

1

Introduction

T h e d e t e r m i n a t i o n of cosmological constant has become one of the m a i n issue of modern physics since by fixing i t s value, one c o u l d c o n t r i b u t e t o select selfconsistent models of fundamental physics a n d cosmology. Briefly, i t s d e t e r m i n a t i o n s h o u l d provide the g r a v i t y v a c u u m state, s h o u l d make to u n d e r s t a n d the mechanism w h i c h l e d the early universe to the t o d a y observed large scale structures a n d to predict what w i l l be the fate of the whole universe ( n o - h a i r conjecture). F r o m the cosmological p o i n t of view, the m a i n feature o f i n f l a t i o n a r y models is the presence of a finite p e r i o d d u r i n g w h i c h the e x p a n s i o n is de S i t t e r (or quasi-de Sitter o r power law): this fact implies t h a t the e x p a n s i o n o f the scale factor a ( t ) is s u p e r l u i n i n a l (at least a ( t ) •» f, i n general a ( t ) — exprYnf where H is the H u b b l e parameter nearly constant for a finite period) w i t h respect to the c o m o v i n g proper t i m e t. S u c h a s i t u a t i o n arises i n presence of a n effective energy m o m e n t u m tensor w h i c h is a p p r o x i m a t e l y p r o p o r t i o n a l (for a certain time) to the metric tensor a n d takes place i n various g r a v i t a t i o n a l theories: i.e. the E i n s t e i n g r a v i t y m i n i m a l l y coupled w i t h a scalar field, fourth or h i g h e r - o r d e r gravity. 0

U s i n g conformal transformations (by w h i c h h i g h e r - o r d e r g e o m e t r i c t e r m s and n o n m i n i m a l l y coupled fields are reduced to the E i n s t e i n g r a v i t y plus m i n i m a l l y coupled scalar fields) a l l of these approaches can furnish d y n a m i c a l models where some scalar fields are displaced from their e q u i l i b r i u m states { f a l s e v a c u u m states) a n d then evolve sufficiently slow t o w a r d the m i n i m a of

51

a potential, i n general t o w a r d new e q u i l i b r i u m states ( t r u e v a c u u m s t a t e s ) . If more t h a n one scalar field undergo such a phenomenology, one can get multiple inflation. Several inflationary models are affected by the s h o r t c o m i n g of "fine t u n ing", t h a t is inflationary phase proceeds from very special i n i t i a l c o n d i t i o n s , while a n a t u r a l issue w o u l d be to get inflationary solutions as a t t r a c t o r s for a large set of i n i t i a l conditions. F u r t h e r m o r e , the same s i t u a t i o n s h o u l d be achieved also i n the future: if a remnant of c o s m o l o g i c a l constant is t o d a y observed, the universe should evolve t o w a r d a final de S i t t e r stage. A more precise f o r m u l a t i o n of such a conjecture is possible for restricted classes of cosmological m o d e l s . W e have to note t h a t the conjecture holds when any o r d i n a r y m a t t e r field satisfies the d o m i n a n t a n d s t r o n g energy c o n d i t i o n s . However it is possible to find models w h i c h e x p l i c i t l y violate such c o n d i t i o n s but satisfies n o - h a i r theorem requests. Precisely, this fact happens if extended gravity theories are involved and m a t t e r is i n the form of scalar fields, besides the o r d i n a r y perfect fluid m a t t e r . 3

In any case, we need a t i m e v a r i a t i o n of cosmological constant to get successful inflationary models, to be i n agreement w i t h observations, a n d to obtain a de S i t t e r stage t o w a r d the future. In other words, this means t h a t cosmological constant lias to acquire a great value i n early epoch (de S i t t e r stage), has to undergo a phase t r a n s i t i o n w i t h a graceful exit (in order t o recover the observed F r i e d m a n stage of present epoch) a n d has to result i n a small r e m n a n t t o w a r d the future. In this context, a fundamental issue is to select the classes of g r a v i t a tional theories and the conditions w h i c h " n a t u r a l l y " allow to recover an effective time-dependent cosmological constant w i t h o u t considering special i n i t i a l data. T h i s work is devoted to this p r o b l e m . We take i n t o consideration extended gravity theories a n d t r y to select conditions to o b t a i n effective t i m e - d e p e n d e n t cosmological constant. T h e m a i n request is t h a t such effective c o s m o l o g i c a l constants evolve (at least a s y m p t o t i c a l l y ) t o w a r d the a c t u a l cosmological constant w h i c h means t h a t the de Sitter behaviour has to be recovered.

2

Recovering the no-hair theorem in extended cosmologies

gravity

T h e r e is no a p r i o r i reason to restrict the g r a v i t a t i o n a l L a g r a n g i a n to a linear function of the R i c c i scalar R m i n i m a l l y c o u p l e d w i t h m a t t e r . A d d i t i o n a l l y , we have to note that, recently, some authors have taken into serious c o n s i d e r a t i o n the idea t h a t there are no "exact" laws o f physics but t h a t the L a g r a n g i a n s of

52 physical interactions are "stochastic" functions w i t h t h e p r o p e r t y t h a t local gauge invariances (i.e. conservation laws) are well a p p r o x i m a t e d i n t h e l o w energy l i m i t a n d p h y s i c a l constants c a n vary. T h i s scheme was a d o p t e d i n order to treat the q u a n t i z a t i o n on c u r v e d space-times and the result was t h a t the interactions a m o n g q u a n t u m scalar fields a n d b a c k g r o u n d geometry or the g r a v i t a t i o n a l self-interactions yield corrective terms i n the E i n s t e i n - H i l b e r t L a g i a n g i a n . F u r t h e r m o r e , it has been realized t h a t such corrective t e r m s are inescapable i f we want to o b t a i n the effective a c t i o n o f q u a n t u m g r a v i t y o n scales closed to the P l a n c k length. T h e y are h i g h e r - o r d e r t e r m s i n c u r v a t u r e invariants as R , WMp, or V(d>) ~ m < p (or the r o n f o r u i a l transformed field p o t e n t i a l s t a r t i n g from theories as R ) , it means, i n our o p i n i o n , t h a t these terms are not so essential for recovering the cosmological constant (in this case from the m a t t e r field side). T e r m s of these k i n d s arise also i n the effective L a g r a n g i a n o f strings a n d K a l u z a - K l e i n theories when the mechanism of dimensional r e d u c t i o n is w o r k i n g . n

2

2

2

F r o m a completely different point of view, these a l t e r n a t i v e theories become interesting when one t r y to i n c o r p o r a t e the M a c h p r i n c i p l e i n g r a v i t y and to consider the concept o f ''inertia" i n connection to the v a r i o u s f o r m u l a t i o n s of equivalence p r i n c i p l e . F o r example, the B r a n s - D i c k e theory is a serious a t t e m p t of alternative theory to the E i n s t e i n g r a v i t y : it takes i n t o c o n s i d e r a tion a variable N e w t o n g r a v i t a t i o n a l constant whose d y n a m i c s is governed by ;i scalar' field n o n m i m n i a l l y coupled w i t h geometry. In such a way, the M a c h principle is betver i m p l e m e n t e d . 5

Here we want to consider such theories, i n general, a n d to ask for recovering the de Sitter behaviour i n the related c o s m o l o g i c a l models. Let us start w i t h the most general class of h i g h e r - o r d e r - s c a l a r - t e n s or theories i n four dimensions. T h e y c a n be assigned by the a c t i o n A = J

d*xsf=-g

[F(/L• « , • * * , . . • * * , * ) - -

^

.

^

+ C ] m

,

(1)

where F is an unspecified function of curvature invariants a n d o f a scalar field (p. T h e t e r m C,„ is the m i n i m a l l y coupled o r d i n a r y m a t t e r c o n t r i b u t i o n . W e shall use physical units 8TIG = c = h = l : e i s a constant w h i c h specifies the

53

theory. W i t h the choice F = M M ~ v U ) ,

=-i,

6

(2)

we recover the s c a l a r - t e n s o r gravity i n w h i c h a scalar field d? is n o n m i n i m a l l y coupled w i t h the R i c c i s c a l a r . Here, we do not fix the c o u p l i n g a n d the p o t e n t i a l V{4>) but we ask for recovering (in general) the de S i t t e r b e h a v i o u r by restoring the cosmic n o - h a i r theorem. A s we shall see, this request w i l l fix a class of couplings a n d potentials. T h e a c t i o n (1) now becomes 5

Jd^xyf^g

A -

(3)

For the sake of simplicity, we develope our considerations i n a F R W flat spacetime, but the results can be easily extended t o any homogeneous cosmological m o d e l i n c l u d i n g also K a n t o w s k i - S a c h s m o d e l s . W e have the line element 1

2

ds

2

2

= d t - a(t) (dx

2

2

+ dy

2

+ dz ),

(4)

where a = a ( t ) is the scale factor of the universe and we get the cosmological equations

H = - (H

H

= -{

2

Hi

•

^

+v)- ff V

H

+

• P

tf--,-i +- ^ I f

, Z

P

m

+ P r .

^

where P ^ = \ ^ p

m

+ V{ 3T7T • 6|/| '

(13)

we o b t a i n H < 0 .

(14)

The universe, for large i , has a de S i t t e r b e h a v i o u r , (i.e.a(f) ~ e x p ( a t ) , where Q is a constant). D u e to the conditions (11), a n d (13), the universe, for large f, expands as de S i t t e r , even if it is not fixed the parameter w h i c h specifies such an expansion, i.e. the effective c o s m o l o g i c a l constant. If we c o m p a r e the conditions i n w i t h ours, we have: 3

( n o - h a i r conditions) >0

H)

H < - - H 0

(our a s y m p t o t i c c o n d i t i o n s ) = f i i ( l - t - A i ) . T h e o n l y s o l u t i o n t o E q . (6) w h i c h is real, positive a n d reproduces the A — 0 case i n the l i m i t of s m a l l An is 3

0

r^v* c o s f * z *

2

=

^ vlU~J 2

2

1

2

(7)

{—)

/2

w i t h 0 = a r c c o s [ s / { i + y ) ' } , x = -9b\ b and y = [3f-4&| w h i l e for An — 0 we s i m p l y get s = —63/62T h e c o n d i t i o n for the general s o l u t i o n (7) to be real is 3

1

2

276 6|)] / , 1

t a

A where

L

> A

i > c r

= i- (Ai)-l p

(8)

123

and 9(Ai) Ai

-

{Ai[8 - Xf + 20Ai + 8(1 - A j )

3 / 2

]}

1 / 3

.

is the c r i t i c a l density for the overdense region t o t u r n a r o u n d .

i C t

(10) I n the

l i m i t o f An - » 0 we have p(Aj) - ¥ 1 a n d we r e p r o d u c e the well k n o w n c o n d i t i o n A >A 1

i ( C r

(A

0

= 0 ) - i - - l .

(11)

After t u r n - a r o u n d the proper size o f the r e g i o n r ( t ) evolves a l m o s t i n d e p e n d e n t l y o f the presence o f the c o s m o l o g i c a l constant a n d c a n be well a p p r o x i m a t e d b y the a n a l y t i c a l solutions for An — 0: r / V t — (1 — cos(7)/2 a n d i f t = (0 - sinS)/(27r) w i t h 0 < 9 < 2%. a

m

4

T h e c h a r a c t e r i s t i c densities

Integrating equations (1) a n d (5) we get f Jo

/(a)do = H t Q

:

f g(s)ds Jo

(12)

= H;t.

E l i m i n a t i n g t we o b t a i n equations w h i c h c a n be used to c a l c u l a t e the scale factor at t u r n - a r o u n d ( a ) a n d collapse ( a i i ) of a region w i t h p a r t i c u l a r A ; at a given z-, t a

co

f

£"f(a)da= ^£°g(s}ds /•Ocelli J

f(a)da

(13)

I I /-Sla = 2-^ J g(s)ds

(14)

where s is g i v e n by E q . (7). A s s u m i n g t h a t the mass inside the overdense region does not change, the overdensity inside the sphere o f size r w i t h respect to the b a c k g r o u n d density at any t i m e is t a

5 = - ^ - l

=

4('-V(l + A

i

) - l .

(15)

A t early t i m e s , t —> 0, we c a n e x p a n d the expressions o n the left-hand sides of b o t h equations i n (12) a r o u n d a = 0 a n d s = 0 respectively. I n t e g r a t i n g t e r m b y t e r m we c a n express t i m e as a power series of a a n d s respectively. I n v e r t i n g those series we o b t a i n a a n d s as power series o f t ^ . I n s e r t i n g t h e m i n t o E q . (15) a n d r e p l a c i n g (-dependence w i t h a we find 2

2

6 = h ( U , X o , Ai,2i)o + 0 { a ) , 0

3

(16)

124

1.70 1.70

1.65

/

rr--

—

f / ft

—

•

il =0.3 x„=o * =0.4 X -0.7 — *„=1 n„=i. \,=o 0

I

1.60

—

J** /

0

p

i

i

1.55

•

J —

4

10

6

2 coll Figure I: Left panel' parameter 5 as a function of flo for I H = 0. Solid lines correspond from bottom to top to Ao = 0,0.2,0.4,0.6,0.8 and 1. The dashed line shows results for the flat case QQ + Ac = 1. Right panel: parameter S as a function of z \\ for four models with Jio = 0.3 and A = 0,0.4,0.7 and 1. The thin straight line marks the fiducial value S = 1.68647 for fi = 1, A = 0. C

CO

C

ca

0

c

0

0

where

h(f! ,A , Ai,zi) 0

0

-

1 - JJQ - AQ

[ f i i ( l + A O + Ai - 1](1 + Zi) ni(i+Ai)V3

(17)

G i v e n the behavior o f the linear g r o w t h factor D ( a ) i n E q . (3), we o b t a i n the density contrast as predicted by linear theory 5

L

= / i ( f i A , Ai,2i)I>(a). 0 l

(18)

a

A p a r t i c u l a r l y useful q u a n t i t y is the linear density contrast at the m o m e n t of collapse i.e. when s reaches zero 6

C

= ii[fl ,A , Ai(a 0

0

c o l

|),Zi]/)(a ii).

(19)

c o

A i ( a „ u ) i n the above equation means t h a t A ; c o r r e s p o n d i n g to a u has t o be d e t e r m i n e d n u m e r i c a l l y for a given z\ from the E q . (14). N u m e r i c a l results for 1 G e V . S t i l l , for the sake o f generality, we have the m u c h more generous b o u n d (10) in F i g . 2 but m a r k e d a l o w range o f m w i t h a light grey b a n d t o i n d i c a t e the above p o i n t . x

2

2

x

a

a

L i k e w i s e , for reheating temperatures j u s t above Tf s t a n d a r d estimates o f f l h become questionable. W e have therefore i n d i c a t e d this range o f T R w i t h again a light g r e y color. It has also been recently p o i n t e d o u t t h a t even i n the case o f v e r y low reheating temperatures T R below the L O S P freezeout t e m p e r a t u r e , a significant p o p u l a t i o n of t h e m w i l l be generated d u r i n g the r e h e a t i n g phase. S u c h L O S P s w o u l d t h e n also decay i n t o axinos as above. 2

x

1 3

144

Figure 2. The thick solid line gives the upper bound from thermal production on the reheating temperature as a function of the axino mass. The dark region is the region where nonthermal production can give cosmologically interesting results ( f t t f i ~ 1) as explained in the text. We assume a bino-like neutralino with m \ — 100 GeV and f — 10" G e V . The region of > T( is somewhat uncertain and has been denoted with light-grey color. A sizeable abundance of neutralinos (and therefore axinos) is expected also for TR < Tf but has not been calculated. The vertical light-grey band indicates that a low range of ma corresponds to allowing S M superpartner masses in the multi-TeV range, as discussed m the text. Division of hut, W H I H I and cold datk niattei by the axino mass shown in lower left part is for axinos from non-thermal production. , T P

a

a

145

We have not considered such cases i n our analysis and a c c o r d i n g l y left the region T R < Tf blank even t h o u g h in p r i n c i p l e we w o u l d expect some sizeable range o f t l h there. We c a n see t h a t for large TR, the T P m e c h a n i s m is more i m p o r t a n t t h a n the N T P one, as expected. N o t e also t h a t in the T P case the cosmo logic ally favored region (0.2 < Q h < 0.4) w o u l d f o r m a v e r y n a r r o w s t r i p (not i n d i c a t e d i n F i g . 2) j u s t below the f i = 1-boundary. I n contrast, the N T P mechanism c a n give the cosmologically interesting range of the a x i n o r e l i c a b u n d a n c e for a relatively wide range o f m so l o n g as T < 5 x 1 0 G e V . P e r h a p s i n t h i s sense, the N T P mechanism c a n be considered as somewhat more r o b u s t . 2

a

2

a

T P

4

a

3.5

R

Conclusions

T h e i n t r i g u i n g p o s s i b i l i t y t h a t the axino is the L S P a n d d a r k m a t t e r possesses a n u m b e r o f v e r y d i s t i n c t features w h i c h makes this case very different from those of b o t h the n e u t r a l i n o and the gravitino. I n p a r t i c u l a r , the a x i n o c a n be a c o l d D M W I M P for a rather w i d e range of masses in the M e V t o G e V range a n d for r e l a t i v e l y low reheating temperatures TR < 5 x 1 0 G e V , A s TR increases, t h e r m a l p r o d u c t i o n of axinos starts d o m i n a t i n g over n o n - t h e r m a l p r o d u c t i o n a n d the axino t y p i c a l l y becomes a w a r m D M relic w i t h a mass b r o a d l y i n a k e V range. In contrast, the neutralino is t y p i c a l l y a cold D M WIMP. 4

Low scale. It it is the problem

reheating temperatures w o u l d favor baryogenesis at the electroweak w o u l d also alleviate the nagging "gravitino p r o b l e m " . If a d d i t i o n a l l y a x i n o t h a t is the L S P a n d the g r a v i t i n o is the N L S P , the g r a v i t i n o is resolved altogether for b o t h low and h i g h T R .

P he nomeno logic ally, one faces a well-justified p o s s i b i l i t y t h a t the b o u n d £l h < 1, w h i c h is often imposed i n c o n s t r a i n i n g a S U S Y parameter space, may be r e a d i l y avoided. In fact, the range S l h 3> 1 (and w i t h i t t y p i c a l l y large masses o f superpartners) w o u l d now be favored if a x i n o is to be a d o m inant c o m p o n e n t o f D M i n the U n i v e r s e . F u r t h e r m o r e , the lightest o r d i n a r y s u p e r p a r t n e r c o u l d either be n e u t r a l or charged b u t w o u l d appear stable i n collider searches. 2

x

2

x

T h e a x i n o , w i t h its exceedingly t i n y c o u p l i n g to other matter, w i l l be a real challenge t o experimentalist. It is m u c h more plausible t h a t a s u p e r s y m m e t r i c p a r t i c l e and the a x i o n w i l l be found first. Unless the neutralino (or some other W I M P ) is detected i n D M searches, the axino w i l l r e m a i n a n a t t r a c t i v e and robust c a n d i d a t e for s o l v i n g the o u t s t a n d i n g puzzle o f the nature o f d a r k m a t t e r i n the U n i v e r s e .

146

References 1. L . C o v i , J . E . K i m a n d L . R o s z k o w s k i , P h y s . R e v . L e t t . 8 2 , 4180 (1999). 2. L . C o v i , H . B . K i m , J . E . K i m and L . R o s z k o w s k i , h e p - p h / 0 1 0 1 0 0 9 . 3. J . E . K i m , P h y s . R e v . L e t t . 4 3 , 103 (1979); M . A . S h i f m a n , V . I . V a i n s t e i n , a n d V . I . Z a k h a r o v , N u c l . P h y s . B 1 6 6 , 4933 (1980). 4. M . D i n e , W . F i s c h l e r , a n d M . S r e d n i c k i , P h y s . L e t t . B 1 0 4 , 99 (1981); A . P . Z h i t n i t s k i i , Sov. J . N u c l . P h y s . 3 1 , 260 (1980). 5. J . E . K i m , P h y s . R e p . 1 5 0 , 1 (1987); M . S . T u r n e r , P h y s . R e p . 1 9 7 , 67 (1990); G . G . Raffelt, P h y s . R e p . 1 9 8 , 1 (1990); P. S i k i v i e , hepph/0002154. 6. K . T a m v a k i s a n d D . W y l e r , P h y s . L e t t . B 1 1 2 , 451 (1982). 7. K . R a j a g o p a l , M . S. T u r n e r , a n d F . W i l c z e k , N u c l . P h y s . B 3 5 8 , 447 (1991). 8. E . J . C h u n , J . E . K i m a n d H . P. N i l l e s , P h y s . L e t t . B 2 8 7 , 123 (1992). 9. P. N a t h and R . A r n o w i t t , P h y s . R e v . L e t t . 6 9 , 725 (92). 10. R . G . R o b e r t s and L . R o s z k o w s k i , P h y s . L e t t . B 3 0 9 , 329 (1993). 11. G . L . K a n e , C . K o l d a , L . R o s z k o w s k i , a n d J . D . W e l l s , P h y s . R e v . D 4 9 , 6173 (1994). 12. J . E l l i s , et a i , N u c l . P h y s . B 3 7 3 , 399 (1992). 13. G . F . G i u d i c e , E . W . K o l b , a n d A . R i o t t o , h e p - p h / 0 0 0 5 1 2 3 .

RECENT

DEVELOPMENTS IN SUPERSYMMETRIC M A T T E R

ACHILLE CORSETTI D e p a r t m e n t of P h y s i c s , N o r t h e a s t e r n B o s t o n , M A 0 2 1 1 5 , USA E-mail: [email protected]

D A R K

University

PRAN NATH D e p a r t m e n t of P h y s i c s , N o r t h e a s t e r n U n i v e r s i t y , B o s t o n , M A 0 2 1 1 5 , U S A " Physikalisches Institut, Universitat B o n n , Nussallee 12, D - 5 3 1 1 5 B o n n , G e r m a n y M a x - P l a n c k - I n s t i t u t e fuer Kernphysik, Saupfercheckweg 1, D - 6 9 1 1 7 Heidelberg, Germany E-mail: [email protected] A brief review is given of some of the recent developments in the theoretical analyses of supersymmetric dark matter. These include the effects of uncertainties in the wimp velocity and wimp density and of the effects of uncertainties in the quark densities of the proton. Also analyzed are the effects of non-universalities in the gaugino sector and their effects on determining the nature of cold dark matter, i.e., if the neutralino is bino like, higgsino like, or wino like. The maximum and the minimum elastic neutralino proton cross sections are discussed and a comparison of the direct and the indirect detection arising from the capture and annihilation of neutralinos in the core of the earth and the sun is given. Some of the other recent developments are summarized.

1

Introduction

Because o f the recent significant a c t i v i t y i n d a r k m a t t e r searches o n the exp e r i m e n t a l s i d e ' there is renewed interest i n the t h e o r e t i c a l analyses o f d a r k m a t t e r w h i c h are s i g n i f i c a n t l y more refined t h a n i n the p r e v i o u s years. A m o n g the refinements is the i n c l u s i o n s o f the effects of u n c e r t a i n t i e s i n the i n p u t parameters i n the t h e o r e t i c a l p r e d i c t i o n s of event rates a n d of the n e u t r a l i n o p r o t o n cross sections as w e l l i n c l u s i o n of the effects of non-universalities, C P v i o l a t i n g effects a n d the effects o f c o a n n i h i l a t i o n . T h e content of the paper is as follows: I n Sec.2 we discuss the effects of uncertainties i n the analyses o f d a r k m a t t e r . T h e s e i n c l u d e the effects o f u n c e r t a i n t i e s i n the w i m p velocity and i n the w i m p relic density, a n d the effects o f uncertainties i n the q u a r k densities i n the p r o t o n i n the analyses of d a r k m a t t e r . I n Sec.3 we give a discussion o f the m a x i m u m a n d the m i n i m u m elastic n e u t r a l i n o - p r o t o n crosssections. I n Sec.4 we discuss the effects of n o n - u n i v e r s a l i t i e s a n d specifically 1

2 , 3

° : Permanent address

147

148

Figure I t An exhibition of the effect of the variation of the wimp velocity and wimp relic density on the event rates in a Ge detector as a function of the fine tuning parameter $. Taken from Ref. 9

the c o n - universalities i n the gaugino sector on dark m a t t e r analyses. A brief discussion of the effects of p o n the c o m p o s i t i o n of the n e u t r a l i n o a n d its role i n d e t e r m i n i n g the n a t u r e of cold d a r k m a t t e r , i.e., i f it is d o m m a n t l y a bino, a w i n o or a higgsino is given i n Sec.5. A c o m p a r i s o n of the direct a n d the indirect d e t e c t i o n of d a r k m a t t e r is given i n Sec.6. I n Sec.7 we give a d i s c u s s i o n of the annual m o d u l a t i o n effect i n the direct d e t e c t i o n of d a r k m a t t e r . I n Sec.8 we give a brief discussion of the effects of C P phases o n d a r k m a t t e r . C o n c l u s i o n s are given i n Sec.9.

2

Uncertainties in Theoretical Analyses of D a r k M a t t e r

T h e direct d e t e c t i o n of d a r k m a t t e r has been investigated b y m a n y a u t h o r s ( see Ref. for some of the recent works). Several types of u n c e r t a i n t i e s enter i n these analyses such as the effects of variations i n the l o c a l w i m p density, the effects of variations i n the w i m p v e l o c i t y range, a n d the effects of u n c e r t a i n ties i n the q u a r k densities i n the nucleons. O t h e r effects not c o n s i d e r e d here are the uncertainties i n the nuclear form factors, and effects o f halo models on the event rates i n d a r k m a t t e r detection. W e b e g i n w i t h a d i s c u s s i o n of the analyses of uncertainties i n w i m p density a n d v e l o c i t y ' . T h e current range of l o c a l w i m p density lies i n the r a n g e (0.2 — 0 . 7 ) G e V c m . D e f i n i n g £ = p ^ i / p o one c a n p a r a m e t e r i z e the local w i m p density i n t e r m o f £ w h i c h for p a = 0 . 3 G e V c m gives 0.7 < £ < 2.3. F o r the w i m p v e l o c i t y one t y p i c a l l y assumes a M a x w e l l i a n v e l o c i t y d i s t r i b u t i o n for the w i m p s . E s t i m a t e s o f the rms w i m p v e l o c i t y range g i v e v = 270 ± 50 k m / s . T h e a n a l y s i s is c a r r i e d out w i t h i n the framework o f the m i n i m a l s u p e r g r a v i t y m o d e l ( S U G R A / . T h e soft S U S Y b r e a k i n g sector i n the m i n i m a l version m S U G R A of t h i s t h e o r y 4

5

5

10

7

8 , 9

- 3

- 3

11

2

149

is given by m n , A Q , a n d tan/3 where, m o is the u n i v e r s a l scalar mass, rrti/2 is the u n i v e r s a l gaugino mass, A is the u n i v e r s a l t r i l i n e a r c o u p l i n g , a n d tan/3 = < H > j < H i > where H gives mass to the u p q u a r k s and H i gives mass to the d o w n q u a r k s a n d the leptons. T h e H i g g s m i x i n g p a r a m e t e r p . is d e t e r m i n e d by the c o n s t r a i n t of r a d i a t i v e b r e a k i n g of the electro-weak s y m m e t r y . It is also useful to define a fine t u n i n g parameter 4> so thafr $ = (p?jM\ + 1/4) ' . T h e fine t u n i n g p a r a m e t e r defines how heavy the S U S Y s p e c t r u m gets. T h e effects of the u n c e r t a i n l y i n the event rate as a function of the fine t u n i n g parameter due to v a r i a t i o n s i n the w i m p relic density a n d i n the w i m p v e l o c i t y are s h o w n i n F i g . l . O n e finds t h a t the effects of this type of u n c e r t a i n t y c a n l e a d to a v a r i a t i o n i n the rates by a factor of 2-3. 0

2

2

3

1

2

9

N e x t we discuss the uncertainties i n neut rah n o - p r o t o n cross-section arising from errors m the q u a r k densities i n the p r o t o n ' ' ' . T h e basic i n t e r a c t i o n governing the x — P s c a t t e r i n g w i t h C P c o n s e r v a t i o n is the four F e r m i interact i o n given b y £ , / / = X T t ^ X T t ^ i A P L + BP )q + Cxxm qq + Dx^X^qQ'TbQFor heavy target m a t e r i a l s the neutralino-nucleus s c a t t e r i n g is d o m i n a t e d b y the scalar i n t e r a c t i o n s w h i c h is c o n t r o l l e d b y the scalar x ~ P cross-section where 1

1

1 5

R

a

x p

(scalar)

= ^

( £

ffC

i

+

1 6

q

^ ( l -

£

ff) £

C

a

f

(1)

Here \ i is the reduced mass and f f (i=u,d,s quarks) are the (u,d,s) q u a r k densities defined by t h p f f = < p|TO t9t9i|j> > (i—u,d,s). I n the above C is the s t r e n g t h of the scalar i n t e r a c t i o n and consists of s channel c o n t r i b u t i o n s from the higgs h°,H° exchange a n d t channel c o n t r i b u t i o n s from the sfermion exchange so t h a t C — C^o + C^a + G i . T h e u n c e r t a i n l y i n the t h e o r e t i c a l predictions of a ( s c a l a r ) is d o m i n a t e d by the u n c e r t a i n t y i n the q u a r k densities ff. T o s t u d y the uncertainties i n f f i t is best first to solve the q u a r k densities a n a l y t i c a l l y i n t e r m s of some j u d i c i o u s l y chosen parameters. O n e finds ' T

q

x p

16 17

where the p a r a m e t e r s

x a n d cr„pj are defined b y

< p \ u u — dd\p > e -

< p \ u u + dd\p > '

< p \ u u + d d — 2ss|p > x =

< p \ u u + dd\p >

_ 1

< p | 2 ( 7 7 i + r n . d ) ( u u + dd\p > = u i v u

T

(3)

150

n

«

*s

IM

,so

m

n, ja*i

Figure 2: The effect on tr value given in Sec.2

x p

of the variations in the quark densities around the centra)

S i m i l a r l y one c a n a n a l y t i c a l l y solve for the q u a r k densities i n the n e u t r o n a n d the a n a l y t i c relations p r o v i d e an interesting c o n n e c t i o n between the q u a r k densities i n the p r o t o n and i n the n e u t r o n . O n e finds t h a t i n d e p e n d e n t of the details of any i n p u t one h a s / ^ / ^ — / " / ^ - O n e c a n use the analysis o n the b a r y o n mass s p l i t t i n g s to determine the r a t i o £ / x . O n e finds f / x — 0.196. U s i n g the d e t e r m i n a t i o n of x from lattice gauge a n a l y s e s one finds f = 0.132 ± 0.035. A d d i t i o n a l uncertainties c a n arise from the q u a r k mass ratios. Here results from c h i r a l p e r t u r b a t i o n t h e o r y ^ give ^ = 0.553 ± 0.043, ^ = 18.9 ± 0.8. U s i n g the i n p u t s above one finds / J = 0.021 ± 0.004, = 61)29 ± 0.006, f f = 0.21 ± 0.12 and / J = 0.016 ± 0.003, Q = 0.037 ± 0.007, = 0.21 ± 0 . 1 2 . 1 6

18

16

1 9 , 7 0 , 2 1

2,23

3

M a x i m u m and M i n i m u m Neutralino-proton Cross Sections

W e discuss now the n u m e r i c a l results of the n e u t r a l i n o p r o t o n cross-sect ions w i t h the quark densities as discussed i n Sec. 2. I n F i g . 2 o- is p l o t t e d exh i b i t i n g the effects o f the v a r i a t i o n s of the q u a r k density as a f u n c t i o n of m . T h e above analysis shows t h a t the \ — p cross section c a n n o t be c o m p u t e d t o an accuracy of b e t t e r t h a n a factoT of 3-5 w i t h the current level o f u n c e r t a i n t i e s in the i n p u t data. F i g . 2 also gives a plot of the m a x i m u m a n d the m i n i m u m of a as a f u n c t i o n o f the n e u t r a l i n o mass. I n the a n a l y s i s of F i g . 2 we have allowed mo a n d to v a r y i n the range up t o 1 T e V a n d the c o n s t r a i n t from the flavor c h a n g i n g n e u t r a l current process b -+ S7 is i m p o s e d . T h e a n a l y s i s of this figure does not i n c l u d e the effects of the s p i n dependent c o n t r i b u t i o n w h i c h could change the scatter plot. Specifically, the m i n i m u m cross sections are sensitive to the i n c l u s i o n of the s p i n dependent p a r t . S i m i l a r analyses c a n be found i n other recent r e f e r e n c e s . x

p

x

x

p

2 4

25,26

151

4

Effects o f Non-universalities o n D a r k M a t t e r

m S U G R A is based o n the a s s u m p t i o n o f a flat K a h l e r p o t e n t i a l . H o w e v e r , the nature of physics at the P l a n c k scale is not fully u n d e r s t o o d . T h u s i n general one s h o u l d allow for the p o s s i b i l i t y of a c u r v e d K a h l e r p o t e n t i a l . T h i s w o u l d lead to non-universalities i n the scalar sector. However, there are stringent constraints on the types of non-universalities allowed i n the scalar sector due to the F C N C c o n s t r a i n t . F o r e x a m p l e , the F C N C constraint i n v e r y s t r o n g o n the a m o u n t of n o n - u n i v e r s a l i t y a l l o w e d i n the first vs the second generation sector. H o w e v e r , this c o n s t r a i n t is not so s t r o n g for the H i g g s sector a n d for the t h i r d generation sector. Effects o f these constraints have been s t u d i e d i n detail i n R e f s . . O n e finds t h a t i n general the presence of non-universalities can increase the cross-sections b y a factor o f 10 or more. 2 7 , 2 8

I n a d d i t i o n t o m o d i f y i n g the K a h l e r p o t e n t i a l P l a n c k scale physics c a n also m o d i f y the gauge k i n e t i c energy f u n c t i o n . I n general the gauge k i n e t i c energy function transforms as the s y m m e t r i c p r o d u c t of two adjoint representations. For the case o f S U { 5 ) one finds t h a t the gauge k i n e t i c energy f u n c t i o n fa/3 transforms as the s y m m e t r i c p r o d u c t o f 2 4 x 2 4 i n S U ( 5 ) w h i c h contains the following i r r e d u c i b l e representations o f S U ( 5 ) : (24 x 2 4 )

s y m m

= 1 + 2 4 + 75 + 2 0 0

(4)

T h e S U ( 5 ) singlet i n the p r o d u c t o n the right h a n d side o f E q . ( 4 ) leads t o a universal gaugino mass while, the a d d i t i o n a l t e r m s generate non-universalities i n the gaugino masses at the G U T scale. T h u s the S U ( 3 ) x SU(2) x U(l) gaugino masses at the G U T scale are i n general a d m i x t u r e s o f a l l the a l l o w e d representations. T h i s a d m i x t u r e leads to the following r e l a t i o n for the gaugino masses at the G U T scale C

m.i{0) = m i ( l + ^ c

r

< )

L

(5)

r r

where n d e p e n d o n one of the representations o n the r i g h t h a n d side i n E q . ( 4 ) and on the subgroup i . I n a d d i t i o n t o the appearance o f gaugino mass non-universalities o f the above t y p e i n s u p e r g r a v i t y models, one also finds q u i t e n a t u r a l l y non-universalities i n a b r o a d class of s t r i n g models: heterotic, H o r a v a - W i t t e n a n d as w e l l i n b r a n e models based o n T y p e l / T y p e I I D s t r i n g c o m p a c t ific at ions. N o w the value of fi is i n general v e r y sensitively dependent on non-universalities. F o r the case o f non-universalities i n the scalar sector one c a n e x h i b i t i n a n a n a l y t i c fashion the dependence of u on n o n - u n i vers ah ties i n

152

ID"*

10"*

I •

10

10 "

m

HO

r.

in

*ao

|C.Y>

Figure 3: Exhibition of the effects of non-universalities on C -J> tralino mass for different values of c?oa-

3

8

a

X

function of the neu-

the Higgs sector and i n the t h i r d generation sector. T h e analysis shows t h a t u is sensitively dependent o n the n o n - u n i v e r s a l i t i e s a n d t h e i r effects c a n signific a n t l y decrease the value of jj. a n d thus affect g a u g i n o vs higgsino c o m p o s i t i o n of the n e u t r a l i n o . A n analysis of the effects o f n o n - u n i v e r s a l i t i e s i n the scalar sector is given i n R e f . . A s i m i l a r p h e n o m e n o n occurs for the case o f gaugino sector non-universalities. Here also one c a n e x h i b i t the dependence o f p. o n non-universalities. O n e finds 27

16

2

c

where d f j . \ / d c - n > 0,6Vi /