The Berry phase in inflationary cosmology

When continuous parameters in a QFT are varied adiabatically, quantum states typically undergo mixing---a phenomenon characterized by the Berry phase. We initiate a systematic analysis of the Berry phase in QFT using standard quantum mechanics methods. We show that a non-trivial Berry phase appears in many familiar QFTs. We study a variety of examples including free electromagnetism with a theta angle, and certain supersymmetric QFTs in two and four spacetime dimensions. We a...

Does inflation provide a compelling explanation for why the universe is so large, so flat, and so old, and a predictive theory of density perturbations? In this brief contribution (based on the role of the author as moderator of the discussion session on inflation), a list of some of the key issues confronting inflationary cosmology will be given, with the hope of focusing the debate on inflation and drawing more attention to some of the potential problems of the inflationary...

A pressing problem in comparing inflationary models with observation is the accurate calculation of correlation functions. One approach is to evolve them using ordinary differential equations ("transport equations"), analogous to the Schwinger-Dyson hierarchy of in-out quantum field theory. We extend this approach to the complete set of momentum space correlation functions. A formal solution can be obtained using raytracing techniques adapted from geometrical optics. We refor...

We propose a new formula for the adiabatic Berry phase which is based on phase-space formulation of quantum mechanics. This approach sheds a new light into the correspondence between classical and quantum adiabatic phases -- both phases are related with the averaging procedure: Hannay's angle with averaging over the classical torus and Berry's phase with averaging over the entire classical phase space with respect to the corresponding Wigner function. Generalizations to the n...

The detected anomalous frequency drift acceleration in Pioneer's radar data finds its explanation in a Berry phase that obtains the quantum state of a photon that propagates within an expanding space-time. The clock acceleration is just the adiabatic expansion rate and an analogy between the effect and Foucault's experiment is fully suggested. In this sense, light rays play a similar role in the expanding space than Foucault's Pendulum does while determining Earth's rotation....

In this paper we present the problem of quantum to classical transition of quantum fluctuations during inflation and in particular the question of evolution of entanglement. After a general introduction, three specific very recent works are discussed in some more detail drawing some conclusion about the present status of these researches.

We consider curved space quantum corrections to the equations of motion of the inflaton field in the early Universe. Using the stochastic formalism in phase space, we demonstrate that the quantum corrected evolution of the inflaton can differ dramatically from its classical evolution when the mass scales in the potential become large, which is naturally the case in fundamental theories describing Planck scale physics. Using the example of the cosine potential, we show that th...

The warm inflation scenario is an alternative mechanism which can explain the isotropic and homogeneous Universe which we are living in. In this work I extend a previously introduced formalism, without the restriction of slow - roll regime. Quantum to classical transition of the fluctuations is studied by means of the "transition function" here introduced. I found that the fluctuations of radiation energy density decrease with time and the thermal equilibrium at the end of in...

In spite of its great phenomenological success, current models of scalar field-driven inflation suffer from important unresolved conceptual issues. New fundamental physics will be required to address these questions. String theory is a candidate for a unified quantum theory of all four forces of nature. As will be shown, string theory may lead to a cosmological background quite different from an inflationary cosmology, and may admit a new stringy mechanism for the origin of a...

These lectures provide a pedagogical introduction to inflation and the theory of cosmological perturbations generated during inflation which are thought to be the origin of structure in the universe.