On inflationary perturbations [Elektronische Ressource] / Vittoria Demozzi. Betreuer: Viatcheslav Mukhanov

Vittoria Demozzi

Sujets

• Physik

Informations

• Publié par: ludwig-maximilians-universitat_munchen
• Publié le: 01 janvier 2011
• Nombre de lectures: 10
• Langue: English

Extrait

On in ationary perturbations
Vittoria Demozzi
Munchen 2011On in ationary perturbations
Vittoria Demozzi
Dissertation
an der Fakult at fur Physik
der Ludwig{Maximilians{Universit at
Munc hen
vorgelegt von
Vittoria Demozzi
aus Trento
Munc hen, den 6. Juni 2011Erstgutachter: Prof. V. Mukhanov
Zweitgutachter: Prof. G. Dvali
Tag der mundlic hen Prufung: 22.07.2011Abstract
In this work we consider di erent aspects of primordial perturbations gener-
ated during in ation. In the rst part we discuss the production of curvature
perturbations. The standard single- eld in ation model predicts almost scale-
invariant adiabatic perturbations which obey Gaussian statistics. This predic-
tion is in very good agreement with the present observational data. However
the measure of the level of non-Gaussianity is not precise yet and a devia-
tion from Gaussianity is allowed. The curvaton scenario, a model of in ation
with two scalar elds, may produce a higher level of non-Gaussianity of the
perturbations than the single- eld model. In this thesis we discuss the super-
curvaton scenario, a curvaton model which naturally appears in the context
of the simplest model of chaotic in ation in supergravity. We compute the
non-linearity parameter f and show that the level of non-Gaussianity canNL
be in the observationally interesting range fromO(10) toO(100).
In the second part we discuss the generation of large-scale magnetic elds from
the ampli cation of quantum uctuations during in ation. We consider a very
broad class of models that can break the conformal invariance of electromag-
netism and therefore give rise to long-wave magnetic elds. We study the e ect
of the back reaction of the generated eld on the background and show that
they can be very important. Assuming that the back reaction does not spoil
in ation and requiring that in ation lasts at least 75 e-folds, we nd a rather
strong restriction on the amplitude of the primordial elds which could be gen-
32erated on in ation. Namely, this amplitude cannot exceed 10 G on Mpc
scales today. This magnetic eld is too small to explain the eld observed in
the Universe and it is too weak also to be ampli ed to the observable values
by the galactic dynamo mechanism.iiContents
1 Introduction 1
2 In ation and perturbation theory 7
2.1 Cosmic evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 In ation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Quantum uctuations in de Sitter spacetime . . . . . . . . . . . . 12
2.4 Linear perturbation theory . . . . . . . . . . . . . . . . . . . . . . 16
2.4.1 Classi cation of the perturbations . . . . . . . . . . . . . . 16
2.4.2 Evolution of the perturbations . . . . . . . . . . . . . . . . 18
2.4.3 Perturbations of a slowly-rolling scalar eld . . . . . . . . 19
2.4.4 Gauge-invariant variables . . . . . . . . . . . . . . . . . . . 23
2.5 Generation of CMB anisotropy . . . . . . . . . . . . . . . . . . . 24
2.6 Non-Gaussian uctuations . . . . . . . . . . . . . . . . . . . . . . 25
2.7 Non-Gaussianity in single- eld in ation . . . . . . . . . . . . . . . 27
2.8 Enhancement of non-Gaussianity after in ation . . . . . . . . . . 29
3 The curvaton scenario 33
3.1 Two- eld in ation . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.1.1 The curvaton eld perturbation . . . . . . . . . . . . . . . 34
3.1.2 The curvature p . . . . . . . . . . . . . . . . . 35
3.1.3 Non-Gaussianity of the curvature perturbation . . . . . . . 38
3.2 The curvaton scenario and supergravity . . . . . . . . . . . . . . . 39
3.2.1 Chaotic in ation in supergravity . . . . . . . . . . . . . . . 40
3.2.2 Supercurvaton . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.2.1 Curvaton perturbations and non-Gaussianity . . 46
iiiCONTENTS
3.2.2.2 Stochastic approach . . . . . . . . . . . . . . . . 47
2 23.2.2.3 A toy model with m =m . . . . . . . . . . . . 49
2 2 9 2 23.2.2.4 m =m + H . . . . . . . . . . . . . . . . . 50 2
2 2 23.2.2.5 m =m +H ; > 0 . . . . . . . . . . . . . . 51
2 2 2 9 2 23.2.2.6 m =m +H + H , > 0 . . . . . . . . . 53 2
2 2 2 9 2 23.2.2.7 m =m +H + H , < 0 . . . . . . . . . 55 2
3.2.2.8 Non-Gaussianity and the curvaton web . . . . . . 56
3.2.2.9 Discussion . . . . . . . . . . . . . . . . . . . . . . 60
4 Magnetic elds in the early Universe 63
4.1 Large-scale magnetic elds in the Universe . . . . . . . . . . . . . 64
4.2 Observational methods . . . . . . . . . . . . . . . . . . . . . . . . 64
4.2.1 Synchrotron emission . . . . . . . . . . . . . . . . . . . . . 64
4.2.2 Faraday rotation . . . . . . . . . . . . . . . . . . . . . . . 64
4.2.3 Zeeman splitting . . . . . . . . . . . . . . . . . . . . . . . 64
4.3 Observations of magnetic elds . . . . . . . . . . . . . . . . . . . 65
4.4 E ects on the Cosmic Microwave Background . . . . . . . . . . . 66
4.4.1 A constant magnetic eld . . . . . . . . . . . . . . . . . . 66
4.4.2 The e ect on the acoustic peaks . . . . . . . . . . . . . . . 67
4.5 Constraints from Big Bang Nucleosynthesis . . . . . . . . . . . . . 69
4.6 Generation of large-scale magnetic elds . . . . . . . . . . . . . . 70
4.6.1 The dynamo mechanism . . . . . . . . . . . . . . . . . . . 71
4.6.2 Primordial vorticity . . . . . . . . . . . . . . . . . . . . . . 72
4.6.3 Magnetic elds from the electroweak phase transition . . . 72
4.6.4 elds from the quark-hadron phase . . 75
4.6.5 Magnetic elds from cosmic strings . . . . . . . . . . . . . 76
5 Large-scale magnetic elds and in ation 77
5.1 Production of magnetic elds during in ation . . . . . . . . . . . 78
5.2 Back reaction of the generated magnetic elds . . . . . . . . . . . 84
5.2.1 Time dependent coupling . . . . . . . . . . . . . . . . . . . 86
5.2.1.1 Strong case . . . . . . . . . . . . . . . . 89
5.2.1.2 Weak coupling case . . . . . . . . . . . . . . . . . 91
ivCONTENTS
5.2.2 Massive eld . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.2.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6 Conclusions 99
References 103
vCONTENTS
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