The Berry phase in inflationary cosmology

This review article aims at presenting the theory of inflation. We first describe the background spacetime behavior during the slow-roll phase and analyze how inflation ends and the Universe reheats. Then, we present the theory of cosmological perturbations with special emphasis on their behavior during inflation. In particular, we discuss the quantum-mechanical nature of the fluctuations and show how the uncertainty principle fixes the amplitude of the perturbations. In a ne...

For a rather general class of scenarios, sweeping through a zero-temperature phase transition by means of a time-dependent external parameter entails universal behavior: In the vicinity of the critical point, excitations behave as quantum fields in an expanding or contracting universe. The resulting effects such as the amplification or suppression of quantum fluctuations (due to horizon crossing, freezing, and squeezing) including the induced spectrum can be derived using the...

We review cosmological inflation and its realization in quantum field theory and in string theory. This material is a portion of a book, also entitled "Inflation and String Theory", to be published by Cambridge University Press.

In this review I consider several different issues related to inflation. I will begin with the wave function of the Universe. This issue is pretty old, but recently there were some new insights based on the theory of the self-reproducing inflationary universe. Then we will discuss stationarity of inflationary universe and the possibility to make predictions in the context of quantum cosmology using stochastic approach to inflation. Returning to more pragmatic aspects of infla...

The standard calculation of the spectrum of density perturbations produced during inflation assumes that there is only one real dynamical degree of freedom during inflation. However, there is no reason to believe that this is actually the case. In this paper we derive general analytic formulae for the spectrum and spectral index of the density perturbations produced during inflation.

This article gives a brief overview of some of the theory behind the inflationary cosmology, and discusses prospects for constraining inflation using observations. Particular care is given to the question of falsifiability of inflation or of subsets of inflationary models.

The spontaneous baryogenesis scenario explains how a baryon asymmetry can develop while baryon violating interactions are still in thermal equilibrium. However, generation of the chemical potential from the derivative coupling is dubious since the chemical potential may not appear after the Legendre transformation. The geometric phase (Pancharatnam-Berry phase) results from the geometrical properties of the parameter space of the Hamiltonian, which is calculated from the Berr...

This is a pedagogical guide to works on this subject which began in the 80s but has seen vibrant activities in the last decade. It aims to help orient readers, especially students, who wish to enter into research but bewildered by the vast and diverse literature on this subject. We describe the three main veins of activities: the Euclidean zero-mode dominance, the Lorentzian interacting quantum field theory and the classical stochastic field theory approaches in some detail, ...

The current status of early universe cosmology can be summarized as precision, but inherently limited, data requiring explanation from precision and robust theory. Specifically inflation is presently the single concrete hope for solving the early universe problem, since it is generically realizable in quantum field theory, but treatment of interactions needs considerable attention. This talk reviews the importance and progress in this direction.

Cosmological phase transitions are thought to have taken place at the early Universe imprinting their properties on the observable Universe. There is strong evidence that, through the dynamics of a scalar field that lead a second order phase transition, inflation shaped the Universe accounting for the most conspicuous features of the observed Universe. It is argued that inflation has also striking implications for the vacuum energy. Considerations for subsequent second order ...