The Invisible Universe: Dark Matter and Dark Energy

437 Pages·2007·6.371 MB·English

by  George Lazarides (auth.), Lefteris Papantonopoulos (eds.)

L. Papantonopoulos (Ed.)
The Invisible Universe:
Dark Matter
and Dark Energy
ABC
Editor
LefterisPapantonopoulos
NationalTechnicalUniversityofAthens
DepartmentofPhysics
ZografouCampus
15780Athens,Greece
[email protected]
L.Papantonopoulos,TheInvisibleUniverse:DarkMatterandDarkEnergy,Lect.Notes
Phys.720(Springer,BerlinHeidelberg2007),DOI10.1007/978-3-540-71013-4
LibraryofCongressControlNumber:2007923172
ISSN0075-8450
ISBN978-3-540-71012-7 SpringerBerlinHeidelbergNewYork
Thisworkissubjecttocopyright. Allrightsarereserved,whetherthewholeorpartofthematerialis
concerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,
reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublication
orpartsthereofispermitted onlyundertheprovisions oftheGermanCopyright LawofSeptember 9,
1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violations
areliableforprosecutionundertheGermanCopyrightLaw.
SpringerisapartofSpringerScience+BusinessMedia
springer.com
(cid:2)c Springer-VerlagBerlinHeidelberg2007
Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,
evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelaws
andregulationsandthereforefreeforgeneraluse.
Typesetting:bytheauthorsandIntegrausingaSpringerLATEXmacropackage
Coverdesign:eStudioCalamarS.L.,F.Steinen-Broo,Pau/Girona,Spain
Printedonacid-freepaper SPIN:12023448 543210
Preface
This book is an edited version of the review talks given in the Third Aegean
SchoolontheInvisibleUniverse:DarkMatterandDarkEnergy,heldinKarfas
onChios Island, Greece,from26thof September to 1stofOctober 2005.The
aim of this book is not to present another proceedings volume, but rather an
advancedmultiauthoredtextbookwhichmeetstheneedsofboththepostgrad-
uate students and the young researchers, in the fields of Modern Cosmology
and Astrophysics.
The issue of dark matter and dark energy is one of the central interest
in Astroparticle Physics, Astrophysics, Astronomy, and Modern Cosmology.
Muchofobservationaldataindicatethatthereisamissingmatterandmissing
energy in the Universe. Evidence of the existence of this unknown form of
matter and energy can be obtained from different sources. In Astrophysics,
thedynamicsofgalaxyformationandgalaxyclusterscangiveinformationon
the amount of missing matter. In Astroparticle physics, particle candidates
wereproposedfromstringtheoryandsupersymmetrytoidentifytheunknown
matter. In Cosmology, the recent data from Cosmic Microwave Background
(CMB) and Supernovae Observations strongly indicate that there is a large
amount of an unknown form of energy in the energy balance of the Universe.
The purpose of this book is to present these issues and discuss in detail the
physics involved.
The first part of the book presents the problem of missing matter of the
Universe as seen by Astroparticle Physics and Astrophysics. G. Lazaride’s
chapter reviews the main proposals of particle physics for the composition of
the dark matter in the universe. The lightest neutralino is the most popular
candidate constituent of dark matter. Axinos and gravitinos can also con-
tribute to dark matter. A model is presented which possesses a wide range
of parameters consistent with the data on dark matter abundance as well as
other phenomenological constraints. In view that many particle theories will
be tested in the next round experiments in large accelerators, such as the
Large Hadron Collider (LHC), a more phenomenological approach to dark
matter in elementary particle physics is adopted in the next chapter by A.
Lahanas. The interest in these experiments is that may provide candidates
for dark matter of supersymmetric origin.
VI Preface
Amoredifficulttaskisundertakeninthenextchapter:thedirectdetection
of supersymmetric dark matter. J. Vergados after reviewing supersymmetric
modelswiththeirparametersconstrainedfromtherecentdataatlowenergies
and cosmological observations, is suggesting experiments of direct detection
of dark matter mainly through a neutralino-nucleus interaction.
The challenge of dark matter is addressed in the context of Astrophysics
by J. Silk’s chapter. It describes the confrontation of structure formation
with observation and it focuses on the detection of the most elusive com-
ponent, non–baryonic dark matter. It explains how galaxy formation theory
is driven by phenomenology and by numerical simulations of dark matter
clustering under gravity. Once the complications of star formation are incor-
porated, the theory becomes very complex. Semi-analytical perspectives of
thetheoryarepresentedthatmayshedsomeinsightintothenatureofgalaxy
formation.
ThesecondpartofthebookdealswiththeenergybalanceoftheUniverse.
InthefirstchapterbyP.Tozzi,thebasicproceduresarepresentedtoconstrain
the cosmological parameters which they describe the energy content of the
Universe.DatafromclustersofgalaxiesandtheirX-raypropertiesareusedas
cosmologicaltoolstodeduceinformationontheseparameters.Thedifficulties
inanalysinggalaxyredshiftsurveysdatalikethe2dFGalaxyRedshiftSurvey
(2dFGRS) and the Sloan Digital Sky survey (SDSS) are explained in W.
Percival’s chapter. A very interesting example is provided of joint analysis of
thelatestCMBandlarge-scalestructuredata,leadingtoasetofcosmological
parameter constraints.
The chapterbyR.Crittendendiscussesthe evidencefordarkenergycom-
ing from a wide variety of data. After reviewing the physics of the CMB,
it discusses the different methods that are used in determining the dark en-
ergy’s density, evolution, and clustering properties and the crucial role the
microwave background plays in all of these methods. L. Perivolaropoulos’s
chapter deals with another interesting manifestation of the presence of dark
energy in the Universe: the late time acceleration. It presents of the recent
observationaldata obtained from type Ia supernovasurveys that support the
accelerating expansion of the universe. The methods for the analysis of the
dataarereviewedandthetheoreticalimplicationsobtainedfromtheiranalysis
are discussed.
The last chapter of the second part of the book by M. Sami is a pre-
sentation of current theoretical models for dark energy. These models rely
on scalar field dynamics and this chapter focusses mainly on the underlying
basic features rather than on concrete scalar field models. The cosmological
dynamics of standardscalarfields,phantoms, andtachyonfields is developed
indetail.Scalingsolutionsarediscussedemphasizingtheirimportanceinmod-
ellingdarkenergy.Thedevelopedconceptsareimplemented inanexampleof
quintessential inflation.
The third part of the book discusses the issue of dark matter and dark
energybeyondthe standardtheoryof GeneralRelativity.Higher dimensional
Preface VII
string and brane theories are employed and also theories that modify the
usual Newtonian dynamics. An introduction to high dimensional theories is
given in I. Antoniadis’ chapter. The basic idea is that the apparent weakness
of gravity can be accounted by the existence of large internal dimensions, in
the submillimeter region, and transverse to a braneworld where our universe
must be confined. The main properties of this scenario are reviewed and its
implications for observationsat both particle colliders and in non-accelerator
gravity experiments are discussed.
These ideas are applied to Cosmology in R. Maartens’ chapter. As ex-
plainedinL.Perivolaropoulos’contributionanacceleratingUniverserequires
thepresenceofadarkenergyfieldwitheffectivelynegativepressure.Analter-
nativetodarkenergyisthatgravityitselfmaybehavedifferentlyfromgeneral
relativity on the largest scales, in such a way as to produce acceleration. In
this chapteranexampleofmodified gravityis presentedwhichis providedby
braneworld models that self-accelerate at late times. The challenges of dark
matter and dark energy in the context of string theory are discussed in N.
Mavromatos’s article. In this chapter the resolution of these issues in string
theoryisbrieflyreviewedandasuggestionfortheresolutionofthedarkenergy
issue is discussed.
The most successful alternative to dark matter in bound gravitational
systems is the modified Newtonian dynamics, or MOND, which is discussed
in R. Sanders’ chapter. There, the various attempts to formulate MOND as
a modification of General Relativity are presented and the covarianttheories
that have been proposed as a basis for this idea are explained. Finally, local
modifications of general relativity by making the Lagrangian an arbitrary
function of the Ricci scalar are presented in R. Woodard’s contribution. The
interestofsuchtheoriesisthattheycanreproducethecurrentphaseofcosmic
acceleration without dark energy.
The Third Aegean School and consequently this book became possible
with the kind support of many people and organizations.The School was or-
ganized by the Physics Department of the National Technical University of
Athens, and supported by the Physics Department of King’s College, Uni-
versity of London, the Institute of Cosmology and Gravitation, University
of Portsmouth, the Physics and Astronomy Department, University of Ten-
nessee.We also receivedfinancialsupportfrom the following sourcesandthis
is gratefully acknowledged:Ministry ofNationalEducationand Religious Af-
fairs, Prefecture of Chios, Municipality of Chios.
WethankGiannisGialasforhisvaluableassistanceandhelpinorganizing
the School in Chios and the University of the Aegean for providing technical
support. We thank also the other members of the Organizing Committee of
theSchool,AlexKehagias,GeorgeKoutsoumbas,GeorgeSiopsis,andNikolas
Tracas for their help in organizing the School. The administrative support
of the Third Aegean School was again taken up with great care by Mrs.
Evelyn Pappa. We acknowledge the help of Vasilis Zamarias, who designed
VIII Preface
andmaintainedthewebsideoftheSchoolandassistedusinresolvingtechnical
issues in the process of editing this book.
Last,but notleast,we aregratefulto the staffofSpringer-Verlag,respon-
sible for the Lecture Notes in Physics, whose abilities and help contributed
greatly to the appearance of this book.
Athens, October 2006 Lefteris Papantonopoulos
Contents
Part I Dark Matter: The Missing Matter of the Universe
as Seen by Astroparticle Physics and Astrophysics
1 Particle Physics Approach to Dark Matter
George Lazarides................................................. 3
1.1 Introduction ................................................ 3
1.2 Axions ..................................................... 4
1.3 Salient Features of MSSM .................................... 6
1.4 Neutralino Relic Abundance .................................. 9
1.5 Axinos ..................................................... 14
1.6 Gravitinos.................................................. 17
1.7 Yukawa Quasi-Unification .................................... 18
1.8 Conclusions................................................. 28
References ...................................................... 29
2 LSP as a Candidate for Dark Matter
Athanasios Lahanas .............................................. 35
2.1 Introduction ................................................ 35
2.2 The Energy – Matter Content of the Universe................... 37
2.3 The Thermal Universe ....................................... 42
2.4 Dark Matter ................................................ 46
2.5 Calculating DM Relic Abundances............................. 48
2.6 Supersymmetry and its CosmologicalImplications ............... 54
2.7 Conclusions................................................. 65
References ...................................................... 66
3 On the Direct Detection of Dark Matter
John Vergados................................................... 69
3.1 Introduction ................................................ 69
3.2 The Nature of the LSP....................................... 72
3.3 The Feynman Diagrams Entering the Direct Detection of LSP .... 72
X Contents
3.4 Going from the Quark to the Nucleon Level..................... 80
3.5 The Nucleon Cross Sections................................... 84
3.6 The Allowed SUSY Parameter Space........................... 84
3.7 Rates ...................................................... 85
3.8 Expressions for the Rates..................................... 87
3.9 Bounds on the Scalar Proton Cross Section ..................... 89
3.10 Exclusion Plots in the a ,a and σ ,σ Planes.................. 90
p n p n
3.11 The Modulation Effect ....................................... 92
3.12 Transitions to Excited States ................................. 93
3.13 The Directional Rates........................................ 93
3.14 Observation of Electrons Produced During
the LSP-nucleus Collisions.................................... 96
3.15 Conclusions................................................. 97
References ...................................................... 98
4 Galaxy Formation and Dark Matter
Joseph Silk......................................................101
4.1 Introduction ................................................101
4.2 Precision Cosmology.........................................102
4.3 The Global Baryon Inventory .................................104
4.4 The “Missing” Baryons ......................................105
4.5 Large-scaleStructure and Cold Dark Matter: The Issues..........106
4.6 Resurrection via Astrophysics .................................107
4.7 What Determines the Mass of a Galaxy? .......................109
4.8 Disk Galaxy Formation ......................................109
4.9 Spheroidal Galaxy Formation .................................111
4.10 Numerical Simulations .......................................112
4.11 The Case for Positive Feedback ...............................115
4.12 Observing Cold Dark Matter: Where Next?.....................117
4.13 Summary...................................................118
References ......................................................119
Part II Dark Energy: The Energy Balance of the Universe
within the Standard Cosmological Model
5 Cosmological Parameters from Galaxy Clusters:
An Introduction
Paolo Tozzi .....................................................125
5.1 Introduction ................................................125
5.2 Clusters of Galaxies in a CosmologicalContext..................126
5.3 From Observations to CosmologicalParameters .................137
5.4 New Physics and Future Prospects.............................149
5.5 What to Bring Home ........................................154
References ......................................................155
Contents XI
6 Cosmological Constraints from Galaxy Clustering
Will Percival ....................................................157
6.1 Introduction ................................................157
6.2 Basics......................................................158
6.3 Matter Perturbations ........................................159
6.4 The Evolution of Perturbations ...............................162
6.5 Galaxy Survey Analysis ......................................165
6.6 Practicalities................................................171
6.7 Results from Recent Surveys..................................174
6.8 Combination with CMB Data.................................175
References ......................................................184
7 Dark Energy and the Microwave Background
Robert Crittenden................................................187
7.1 Introduction ................................................187
7.2 Models for Dark Energy......................................189
7.3 The Physics of the Microwave Background......................192
7.4 Ways of Probing Dark Energy.................................204
7.5 The Integrated Sachs-Wolfe Effect .............................209
7.6 Conclusions and Future Prospects .............................212
References ......................................................214
8 Models of Dark Energy
M. Sami ........................................................219
8.1 Glimpses of FRW Cosmology .................................220
8.2 CosmologicalConstant Λ.....................................236
8.3 Dynamically Evolving Scalar Field Models of Dark Energy........239
8.4 Scaling Solutions in Models of Coupled Quintessence.............248
8.5 Quintessential Inflation.......................................249
8.6 Conclusions.................................................254
References ......................................................255
9 Accelerating Universe: Observational Status
and Theoretical Implications
Leandros Perivolaropoulos.........................................257
9.1 Introduction ................................................257
9.2 Expansion History from the Luminosity Distances of SnIa ........258
9.3 ObservationalResults ........................................265
9.4 Dark Energy and Negative Pressure............................269
9.5 Dynamical Evolution of Dark Energy ..........................278
9.6 The Fate of a Phantom Dominated Universe: Big Rip ............282
9.7 Future Prospects-Conclusion..................................284
References ......................................................287
XII Contents
Part III Dark Matter and Dark Energy Beyond the Standard
Theory of General Relativity
10 The Physics of Extra Dimensions
Ignatios Antoniadis ..............................................293
10.1 Introduction ................................................293
10.2 Framework .................................................295
10.3 Experimental Implications in Accelerators ......................297
10.4 Supersymmetry in the Bulk and Short Range Forces .............302
10.5 ElectroweakSymmetry Breaking ..............................306
10.6 Standard Model on D-branes..................................309
10.7 Non-compact Extra Dimensions and Localized Gravity ...........312
References ......................................................319
11 Dark Energy from Brane-world Gravity
Roy Maartens ...................................................323
11.1 Introduction ................................................323
11.2 KK Modes of the Graviton ...................................326
11.3 DGP Type Brane-worlds:Self-accelerating Cosmologies ..........327
11.4 Conclusion .................................................331
References ......................................................331
12 The Issue of Dark Energy in String Theory
Nick Mavromatos ................................................333
12.1 Introduction ................................................333
12.2 De Sitter (dS) Universes from a Modern Perspective .............336
12.3 No Horizons in Perturbative (Critical) String Theory ............343
12.4 Dilaton Quintessence in String Theory .........................346
12.5 Conclusions.................................................369
References ......................................................372
13 Modified Gravity Without Dark Matter
Robert Sanders ..................................................375
13.1 Introduction ................................................375
13.2 The Phenomenology of MOND................................377
13.3 Relativistic MOND ..........................................385
13.4 TeVeS: Successes, Issues and Modifications .....................393
13.5 Conclusions.................................................398
References ......................................................400
14 Avoiding Dark Energy with 1/R Modifications of Gravity
Richard Woodard ................................................403
14.1 Introduction ................................................403
14.2 The Theorem of Ostrogradski.................................407
14.3 Common Misconceptions .....................................410