The Berry phase in inflationary cosmology

In this paper, it is pointed out that the Berry's phase is a good index of degree of no-commutativity of the quantum statistical model. Intrinsic relations between the `complex structure' of the Hilbert space and Berry's phase is also discussed.

We give a consistent description of how the inflationary Universe emerges in quantum cosmology. This involves two steps: Firstly, it is shown that a sensible probability peak can be obtained from the cosmological wave function. This is achieved by going beyond the tree level of the semiclassical expansion. Secondly, due to decoherence interference terms between different semiclassical branches are negligibly small. The results give constraints on the particle content of a uni...

I argue that cosmological data from the epoch of primordial inflation is catalyzing the maturation of quantum gravity from speculation into a hard science. I explain why quantum gravitational effects from primordial inflation are observable. I then review what has been done, both theoretically and observationally, and what the future holds. I also discuss what this tells us about quantum gravity.

We discuss the effects of cosmic phase transition on the spectrum of primordial gravitational waves generated during inflation. The energy density of the scalar condensation responsible for the phase transition may become sizable at the epoch of phase transition, which significantly affects the evolution of the universe. As a result, the amplitudes of the gravitational waves at high frequency modes are suppressed. Thus the gravitational wave spectrum can be a probe of phase t...

We calculate the quantum gravitational corrections to the Mukhanov-Sasaki equation obtained by the canonical quantization of the inflaton-gravity system. Our approach, which is based on the Born-Oppenheimer decomposition of the resulting Wheeler-DeWitt equation, was previously applied to a minimally coupled inflaton. In this article we examine the case of a non minimally coupled inflaton and, in particular, the induced gravity case is also discussed. Finally, the equation gov...

The first aim of this lecture is to highlight two areas of recent progress in inflationary cosmology, namely reheating and the quantum theory of cosmological perturbations. The second aim is to discuss important conceptual problems for the current realizations of inflation based on fundamental scalar matter fields, and to present some new approaches at solving these problems.

This article gives a brief overview of the status of attempts to constrain inflation using observations, and examines prospects for future developments.

The derivation of the angular spectrum of temperature perturbations of the cosmic microwave background relies on the quantization of field and metric perturbations in the inflationary phase. The quantization procedure thus deserves a close examination. As the background spacetime on which the degrees of freedom that are quantized live is curved, the methods of quantum field theory in curved spacetimes are applicable. Furthermore the dynamic system that is quantized contains a...

Inflationary cosmology has become one of the cornerstones of modern cosmology. Inflation was the first theory within which it was possible to make predictions about the structure of the Universe on large scales, based on causal physics. The development of the inflationary Universe scenario has opened up a new and extremely promising avenue for connecting fundamental physics with experiment. This article summarizes the principles of inflationary cosmology, discusses progress i...

We review some recent progress in the extraction of inflationary observables in loop quantum cosmology. Inverse-volume quantum corrections induce a growth of power in the large-scale cosmological spectra and are constrained by observations.