Quantum Effects in Friedmann-Robertson-Walker Cosmologies

TL;DR

This paper investigates quantum effects on scalar fields in expanding cosmological models, deriving one-loop equations, solving for particle production, and exploring implications for early universe reheating.

Contribution

It introduces a non-local correction to the effective potential in Friedmann-Robertson-Walker cosmologies and analyzes its physical implications.

Findings

Non-local correction modifies the effective potential without changing minima.

Dissipative term relates to scalar field decay and reheating.

Numerical solutions for Bogoliubov coefficients in exponential expansion.

Abstract

Electrodynamics for self-interacting scalar fields in spatially flat Friedmann-Robertson-Walker space-times is studied. The corresponding one-loop field equation for the expectation value of the complex scalar field in the conformal vacuum is derived. For exponentially expanding universes, the equations for the Bogoliubov coefficients describing the coupling of the scalar field to gravity are solved numerically. They yield a non-local correction to the Coleman-Weinberg effective potential which does not modify the pattern of minima found in static de Sitter space. Such a correction contains a dissipative term which, accounting for the decay of the classical configuration in scalar field quanta, may be relevant for the reheating stage. The physical meaning of the non-local term in the semiclassical field equation is investigated by evaluating this contribution for various background field configurations.