Semiclassical Equations for Weakly Inhomogeneous Cosmologies

TL;DR

This paper derives semiclassical Einstein equations incorporating quantum effects of a scalar field in weakly inhomogeneous cosmologies, providing insights into quantum backreaction in early universe models.

Contribution

It introduces a method to compute the quantum stress tensor and backreaction effects in cosmological settings using the in-in effective action formalism.

Findings

Derived the stress tensor for a scalar field around a cosmic string

Computed quantum corrections to Einstein's equations in cosmological models

Analyzed particle creation probabilities in curved spacetime

Abstract

The in-in effective action formalism is used to derive the semiclassical correction to Einstein's equations due to a massless scalar quantum field conformally coupled to small gravitational perturbations in spatially flat cosmological models. The vacuum expectation value of the stress tensor of the quantum field is directly derived from the renormalized in-in effective action. The usual in-out effective action is also discussed and it is used to compute the probability of particle creation. As one application, the stress tensor of a scalar field around a static cosmic string is derived and the backreaction effect on the gravitational field of the string is discussed.