The Berry phase in inflationary cosmology

Inflation in the early Universe is one of the most promising probes of gravity in the high-energy regime. However, observable scales give access to a limited window in the inflationary dynamics. In this essay, we argue that quantum corrections to the classical dynamics of cosmological fields allow us to probe much earlier epochs of the inflationary phase and extend this window by many orders of magnitude. We point out that both the statistics of cosmological fluctuations at o...

We study the out of equilibrium dynamics of inflationary phase transitions and compute the resulting spectrum of metric perturbations relevant to observation. We show that simple single field models of inflation may produce an adiabatic perturbation spectrum with a blue spectral tilt and that the precise spectrum depends on initial conditions at the outset of inflation.

We study the Wigner function for the inflationary tensor perturbation defined in the real phase space. We compute explicitly the Wigner function including the contributions from the cubic self-interaction Hamiltonian of tensor perturbations. Then we argue that it is no longer an appropriate description for the probability distribution in the sense that quantum nature allows negativity around vanishing phase variables. This comes from the non-Gaussian wavefunction in the mixed...

In this letter, we elaborate on the identification and construction of the differential geometric elements underlying Berry's phase. Berry bundles are built generally from the physical data of the quantum system under study. We apply this construction to typical and recently investigated systems presenting Berry's phase to explore their geometric features.

These lectures are intended to give a pedagogical introduction to the main current picture of the very early universe. After elementary reviews of general relativity and of the standard Big Bang model, the following subjects are discussed: inflation, the classical relativistic theory of cosmological perturbations and the generation of perturbations from scalar field quantum fluctuations during inflation.

I discuss how parameters describing inflation in the very early universe may be related to primordial perturbation spectra. Precision observations of anisotropies in the cosmic microwave background (CMB) such as those provided by the WMAP satellite offer an unprecedented window onto the physics of the very early universe. To theorists exploring speculative models of physics at high energies, the CMB offers us the chance to put our ideas to the test.

The purpose of the paper, of which this is part II, is to review, clarify, and critically analyse modern mathematical cosmology. The emphasis is upon mathematical objects and structures, rather than numerical computations. Part II provides a critical analysis of inflationary cosmology and quantum cosmology, with particular attention to the claims made that these theories can explain the creation of the universe.

In this review, we discuss how non-Gaussianity of cosmological perturbations arises from inflation. After introducing the in-in formalism to calculate the $n$-point correlation function of quantum fields, we present the computation of the bispectrum of the curvature perturbation generated in general single field inflation models. The shapes of the bispectrum are compared with the local-type non-Gaussianity that arises from non-linear dynamics on super-horizon scales.

These lecture notes intend to form a short pedagogical introduction to inflationary cosmology, highlighting selected areas of recent progress such as reheating and the theory of cosmological perturbations. Problems of principle for inflationary cosmology are pointed out, and some new attempts at solving them are indicated, including a nonsingular Universe construction by means of higher derivative terms in the gravitational action, and the study of back-reaction of cosmologic...

This article contains a concise review of the theory of inflation. We discuss its main theoretical aspects as well as its observational predictions. We also explain how the most recent astrophysical observations constrain the inflationary scenario.