Inflationary Cosmology

438 Pages·2010·6.553 MB·English

by  Lemoine M., Martin J., Peter P. (eds.)

Editors
Martin Lemoine Jerome Martin
CNRS - Universitd Pierre et Marie Curie CNRS - Universi0 Pierre et Marie Curie
Institut Astrophysiquc de Paris (TAP) Institut d'Astrophysique do Paris (lAP)
98 bd. Arago 98 Boulevard Arago
75014 Paris, France 75014 Paris, France
lemoine@ iap.fr [email protected]
Patrick Peter
CNRS - Universit Pierre et Marie Curie
Institut d'Astrophysique de Paris (1AP)
98 Boulevard Arago
75014 Paris, France
M. Lemoine et al. (Eds.), inflationary Cosmology Lect. Notes Phys. 738 (Springer,
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ISSN 0075-8450
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Preface
A seminal paper, dated 1981, marked the birth of what was to become the
mostsuccessfulparadigminmoderncosmologyfollowingthatofthebigbang
itself: inflation. Its 25th birthday offered a welcome opportunity to celebrate
the phenomenologicalsuccessofinflationandto gather the worldleading sci-
entists engaged in forefront research in this field. Such was the objective of
the XXII IAP colloquium, which took place at “Institut d’Astrophysique de
Paris” (IAP) in June 2006. During this meeting and the immediately follow-
ing two-week workshop, scientists from the world over and from both obser-
vational and theoretical communities gathered to discuss the present status,
the achievements and the shortcomings as well as the future of the theory
of inflation. The numerous discussions that took place offered solid ground
for the publication of regular proceedings. However, inflationary cosmology
encompasses different disciplines of physics, from high energy physics to ob-
servational astrophysics, and it has also become a field of researchin its own
right. Therefore it was felt that a more pedagogical text, containing exhaus-
tive discussions of the ins and outs of inflation, would be more useful. This is
precisely what this present volume of the Lecture Notes in Physics series is
aiming at.
As is by now well known, cosmic inflation corresponds to an episode of
accelerated expansion in the very early Universe which solves the handful of
puzzles that plague the standard hot big bang cosmology, namely the flat-
ness, horizon, monopole excess problems, and, in some models, the problem
oftheprimordialsingularity.Theseachievementsevencomewithabonus:the
production of density perturbations to the level needed to explain the origin
of large scale structure of the Universe. The first chapter of this volume, by
A.Linde,introducesthisframework,offersahistoricaloverviewofthissubject
and develops the present status of the theory. This is followed L. Kofmann’s
discussion on preheating which describes how matter and radiation can have
been producedduring this period which smoothly connects inflation with the
standard big bang phase.
VI Preface
Any cosmological model needs to be implemented in a particle physics
context. The contribution of D. Lyth shows how this can be done in the
most reasonable extensions of the standard particle physics model, namely
those based on supersymmetry. This chapter is followed by the discussion of
R. Kallosh on the embedding of inflation in string theories.
As of today, there are various ways of implementing inflation. One such
framework is “eternal inflation”, in which different parts of the Universe un-
dergo an episode of inflation at different times, the Universe being eternally
inflating and self-reproducing. This particular scenario is discussed in length
by S. Winitzki
As shownby J.Martinin asubsequentchapter,the productionof density
perturbations during inflation is akin to the production of charged particles
out of the vacuum in a strong electric field. This analogy is developed in full
detailinordertoexplainthe inflationaryoriginofprimordialdensity fluctua-
tions.Thenumericalimplementationofthecalculationoftheseperturbations,
whichisrequiredinordertocomparetheseresultstothehighaccuracydataof
cosmic microwavebackground fluctuations, is then discussed by C. Ringeval.
Thenextchapter,byD.Wands,discussesthemodelscontainingmorethan
onescalarfield,inparticulartheirdynamicsandtheobservationalpredictions;
the curvatonmodelis herereviewedasanalternativeto the pure inflationary
productionof perturbations. Then, A. Riotto shows that the measurementof
non-Gaussianities in the spectrum of inflationary perturbations could offer a
way of discrimating the different models.
Finally the possibility of finding alternative scenariosto inflation is a ma-
jor but unanswered issue. The old contender, in which topological defects
seedthe primordialdensity fluctuations has been shownto disagreewith cos-
mic microwave background data. However, as M. Sakellariadou argues, such
topological defects might still be present in our Universe as they should be
producedinconvincingmodelsofinflation.Theircontributiontotheobserved
fluctuations might open a window on physics of an otherwise inaccessible en-
ergy scale. R. Brandenberger concludes this volume by presenting a radically
different perspective in which string gas cosmology plays the main role and
by pointing out some shortcomings of inflation which may argue for the need
of a broader conceptual framework.
Paris, Martin Lemoine, J´eroˆme Martin & Patrick Peter.
April 2007
Contents
1 Inflationary Cosmology
Andrei Linde .................................................... 1
1.1 Brief History of Inflation ..................................... 1
1.2 Chaotic Inflation............................................ 3
1.3 Hybrid Inflation............................................. 9
1.4 Quantum Fluctuations and Density Perturbations .............. 10
1.5 Creation of Matter After Inflation: Reheating and Preheating..... 13
1.6 Eternal Inflation ............................................ 15
1.7 Inflation and Observations ................................... 18
1.8 Alternatives to Inflation?..................................... 21
1.9 Naturalness of Chaotic Inflation............................... 26
1.10 Chaotic Inflation in Supergravity.............................. 28
1.11 Towards Inflation in String Theory ............................ 30
1.12 Scale of Inflation, the Gravitino Mass, and the Amplitude
of the GravitationalWaves ................................... 35
1.13 Initial Conditions for the Low-Scale Inflation and Topology
of the Universe ............................................. 38
1.14 Inflationary Multiverse, String Theory Landscape
and the Anthropic Principle .................................. 40
1.15 Conclusions ................................................ 46
References ...................................................... 47
2 Preheating After Inflation
Lev Kofman..................................................... 55
2.1 Generalities: Reheating the Universe........................... 55
2.2 Pair Creation by an Electric Field............................. 58
2.3 Linear Resonant Preheating .................................. 59
2.4 Non-linear Dynamics of Resonant Preheating ................... 61
2.5 Inflaton Fragmentation ...................................... 64
2.6 Equation of State During Preheating .......................... 68
2.7 Effects of Trilinear Interactions ............................... 69
VIII Contents
2.8 Modulated Fluctuations from Preheating....................... 71
2.9 Reheating After String Theory Inflation........................ 73
2.10 Gravitational Waves from Preheating .......................... 73
2.11 Looking Toward the Future................................... 74
References ...................................................... 78
3 Particle Physics Models of Inflation
David H. Lyth ................................................... 81
3.1 Introduction................................................ 81
3.2 Beyond the Standard Model .................................. 82
3.3 The Initial Condition for Observable Inflation................... 83
3.4 Slow-roll inflation ........................................... 85
3.5 Modular Inflation ........................................... 93
3.6 Small-Field Models.......................................... 95
3.7 Supersymmetry: General Features ............................. 97
3.8 Supersymmetry: Form of the Potential......................... 99
3.9 One-Loop Correction ........................................100
3.10 Small-Field Models: Moving Away from the Origin ..............102
3.11 Moving Toward the Origin; Power-LawPotential................103
3.12 F and D Term Inflation......................................105
3.13 Tree-Level Hybrid Inflation...................................107
3.14 Running Mass Models .......................................109
3.15 Large-Field Models..........................................111
3.16 Warm Inflation .............................................112
3.17 Present Status and Outlook ..................................113
References ......................................................115
4 Inflation in String Theory
Renata Kallosh ..................................................119
4.1 Introduction................................................119
4.2 Cosmology and Particle Physics Phenomenology ................122
4.3 String Theory Inspired Supergravity Models and Cosmology......124
4.4 Brane Inflation in String Theory .............................131
4.5 Modular Inflation in String Theory ............................136
4.6 N-flation/Assisted Inflation ..................................147
4.7 Discussion..................................................150
References ......................................................153
5 Predictions in Eternal Inflation
Sergei Winitzki ..................................................157
5.1 Eternal Inflation ............................................157
5.2 Stochastic Approach to Inflation ..............................166
5.3 Predictions and Measure Issues ...............................177
References ......................................................187
Contents IX
6 Inflationary Perturbations: The Cosmological
Schwinger Effect
J´eroˆme Martin ..................................................193
6.1 Introduction................................................193
6.2 The Schwinger Effect ........................................195
6.3 Quantization of a Free Scalar Field in Curved Space–Time .......204
6.4 Inflationary Cosmological Perturbations of Quantum-Mechanical
Origin .....................................................219
6.5 The Classical Limit of Quantum Perturbations..................229
6.6 Conclusions ................................................237
References ......................................................239
7 The Numerical Treatment of Inflationary Models
Christophe Ringeval ..............................................243
7.1 Motivations ................................................243
7.2 Multifield Inflation ..........................................247
7.3 Numerical Method ..........................................253
7.4 Application to CMB Data Analysis............................262
7.5 Conclusion .................................................269
References ......................................................271
8 Multiple Field Inflation
David Wands....................................................275
8.1 Introduction................................................275
8.2 Homogeneous Scalar Field Dynamics ..........................276
8.3 Primordial Perturbations from Inflation........................280
8.4 Perturbations from Two-Field Inflation ........................287
8.5 Non-Gaussianity ............................................293
8.6 Curvaton Scenario...........................................296
8.7 Conclusions ................................................301
References ......................................................302
9 The Quest for Non-gaussianity
Antonio Riotto ..................................................305
9.1 Introduction:WhyIsitsoInterestingtoMeasureNon-gaussianity
in CosmologicalPerturbations? ...............................305
9.2 What Is Non-gaussianity? ....................................309
9.3 Linear Perturbations on Large Scales ..........................316
9.4 Non-linear Perturbation on Large Scales: Generation of NG ......318
9.5 What Do We Learn from What We Have Done so Far? ..........323
9.6 Observational Constraints on NG in the CMB ..................324
9.7 Towards the Second-Order Transfer Function ...................355
References ......................................................358
X Contents
10 Production of Topological Defects at the End of Inflation
Mairi Sakellariadou ..............................................359
10.1 Introduction................................................359
10.2 CosmologicalInflation .......................................360
10.3 Topological Defects in GUTs .................................367
10.4 BraneworldCosmology ......................................374
10.5 Observational Consequences ..................................377
10.6 Conclusions ................................................389
References ......................................................390
11 ConceptualProblemsofInflationary CosmologyandaNew
Approach to Cosmological Structure Formation
Robert H. Brandenberger..........................................393
11.1 Introduction................................................393
11.2 Problems of Scalar Field-Driven Inflation.......................394
11.3 String Gas Cosmology .......................................400
11.4 String Gas Cosmology and Structure Formation.................408
11.5 Discussion..................................................418
References ......................................................419
Index..........................................................425