Cosmological backreaction of a quantized massless scalar field

TL;DR

This paper investigates the backreaction of a quantized massless scalar field in cosmology, deriving a new differential equation for vacuum energy density and analyzing its implications during inflation and subsequent evolution.

Contribution

It introduces a novel differential equation for vacuum energy density considering adiabatic regularization and validates it across different cosmological backgrounds.

Findings

Vacuum energy obeys a new differential equation depending on a dimensionless parameter.

Backreaction effects are negligible during inflation but may influence later cosmological stages.

Vacuum energy decreases slower than radiation or dust after inflation.

Abstract

We consider the backreaction problem of a quantized minimally coupled massless scalar field in cosmology. The adiabatically regularized stress-energy tensor in a general Friedmann-Robertson-Walker background is approximately evaluated by using the fact that subhorizon modes evolve adiabatically and superhorizon modes are frozen. The vacuum energy density is verified to obey a new first order differential equation depending on a dimensionless parameter of order unity, which calibrates subhorizon/superhorizon division. We check the validity of the approximation by calculating the corresponding vacuum energy densities in fixed backgrounds, which are shown to agree with the known results in de Sitter space and space-times undergoing power law expansions. We then apply our findings to slow-roll inflationary models. Although backreaction effects are found to be negligible during the near exponential expansion, the vacuum energy density generated during this period might be important at later stages since it decreases slower than radiation or dust.