Limitations of the single-eld picture

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Table of contents

Introduction
I The cosmological paradigm
1 The homogeneous and isotropic Universe
1.1 Special Relativity and General Relativity: a description of spacetime
1.1.1 Interferometer experiments and the constancy of the speed of light
1.1.2 Special Relativity: a consistent framework for particles, challenged by gravity
1.1.3 General relativity and the bending of spacetime
1.2 Cosmology: the Universe has a history
1.2.1 Expansion of the Universe, from philosophy to modern science .
1.2.2 Modern approach to cosmology
1.2.3 A brief reverse history of 13.8 billion years
2 Cosmological perturbation theory
2.1 Perturbing spacetime
2.2 Perturbing the matter content
2.2.1 Perturbations of perfect uids
2.2.2 Covariant perturbations of scalar elds
2.3 Gauge freedom and gauge-invariant quantities
2.3.1 Generalities
2.3.2 Spacetime
2.3.3 Matter content
2.3.4 Popular gauges and relations with gauge-invariant variables
2.4 ADM formalism and constraint equations
II Canonical ination: a classical background and quantum pertur- bations
3 Single-eld ination, the minimal working example
3.1 Why ination? The puzzles of the standard Hot Big Bang scenario
3.2 Dynamics of single-eld ination
3.2.1 Background
3.2.2 Linear perturbations
3.3 CMB observations and constraints on single-eld models
3.4 The eective eld theory of ination: a model-independent theory of uctuations
3.4.1 Action in the unitary gauge
3.4.2 Action for the pseudo-Goldstone
4 Multield ination: exploring implications from high-energy physics
4.1 Motivations
4.1.1 Indirect motivations: limitations of the single-eld picture
4.1.2 Direct motivations for multi-scalar ination
4.2 Dynamics of multield ination
4.2.1 Background
4.2.2 Linear perturbations
4.3 The adiabatic-entropic decomposition
4.3.1 A new parameterisation
4.3.2 Super-Hubble evolution and power spectra at the end of ination .
4.3.3 Possible multield instabilities
5 Primordial non-Gaussianities as a probe of extra particle content
5.1 Formalism and generalities
5.1.1 Correlation functions as a parameterisation of Non-Gaussianities .
5.1.2 Primordial non-Gaussianities in single-eld ination
5.1.3 Primordial non-Gaussianities in multield ination
5.1.4 Observational constraints
5.2 Transient tachyonic instability and enhanced non-Gaussianities inattened congurations (article)
5.3 Revisiting non-Gaussianity in multield ination with curved eld space .
5.3.1 Two-eld case (article)
5.3.2 General case with Neld scalars (article)
III Stochastic ination: a non-perturbative treatment of large-scal uctuations
6 Single-eld, slow-roll stochastic ination
6.1 Coarse-graining and the emergence of stochasticity
6.1.1 A separation of scales
6.1.2 Langevin equation: a stochastic dierential equation
6.2 Correlation functions
6.2.1 Fokker-Planck equation and test scalar elds in de Sitter
6.2.2 Cosmological observables in stochastic ination
7 Multield stochastic ination: a path to the discretisation ambiguity and its resolution
7.1 Inationary stochastic anomalies, or the discretisation ambiguity (article)
7.2 A manifestly covariant, anomaly-free theory of multield stochastic ination (article)
IV Cosmological reheating: the transition
8 Single-eld (p)reheating and the growth of small-scale perturbations
8.1 Generalities and growth of small-scale perturbations during (p)reheating (article)
8.2 Metric preheating and formation of Primordial Black Holes
8.3 Temperature of reheating
9 Multield { multi-uids reheating and the evolution of isocurvature perturbations
9.1 General formalism and application to double ination (article)
9.2 Going further: a few possibilities
Conclusion and prospects
Compte-rendu en francais
Bibliography