Backreaction of a massless minimally coupled scalar field from inflationary quantum fluctuations

TL;DR

This paper investigates the quantum backreaction of a massless scalar field during different cosmological eras, revealing a tiny but persistent quantum energy density that may influence dark matter.

Contribution

It provides a detailed calculation of the one-loop quantum energy-momentum tensor across inflation, radiation, and matter eras using a sudden matching approximation.

Findings

Quantum energy density grows logarithmically during radiation era.

Quantum to classical energy ratio stabilizes at ~10^(-13) in matter era.

Quantum fluctuations may contribute to dark matter if clustering conditions are met.

Abstract

In this paper we study a massless, minimally coupled scalar field in a FLRW spacetime with periods of different constant deceleration parameter. We assume the Bunch-Davies vacuum during inflation and then use a sudden matching approximation to match it onto radiation era and subsequently onto matter era. We then proceed to calculate the one-loop energy-momentum tensor from the inflationary quantum vacuum fluctuations in different eras. The energy-momentum tensor has the form of an ideal (quantum) fluid, characterized by an equation of state. When compared with the background, far away from the matching the quantum energy density in radiation era exhibits a contribution that grows logarithmically with the scale factor. In matter era the ratio of the quantum to classical fluid settles eventually to a tiny constant, (rho_q) / (rho) = 10^(-13) for a grand unified scale inflation. Curiously, the late time scaling of quantum fluctuations suggests that they contribute a little to the dark matter of the Universe, provided that it clusters as cold dark matter, which needs to be checked.