Second-order energy-momentum tensor of a scalar field

TL;DR

This paper analyzes the second-order effective energy-momentum tensor of a scalar field during inflation, revealing its gauge dependence and its behavior as an effective fluid with w=-1/3 on large scales.

Contribution

It provides a detailed study of the gauge dependence of the second-order energy-momentum tensor in scalar field cosmology during inflation.

Findings

2EMT is gauge dependent.

2EMT behaves as a fluid with w=-1/3 on super-horizon scales.

The behavior is consistent across multiple gauge choices.

Abstract

We investigate the second-order effective energy-momentum tensor (2EMT) constructed by the quadratic terms of the linear scalar cosmological perturbations while the universe is dominated by a scalar field. We show that 2EMT is gauge dependent. We then study 2EMT in three (longitudinal, spatially flat, and comoving) gauge conditions in the slow-roll stage of inflation. We find that 2EMT exhibits an effective fluid of w=-1/3 on super-horizon scales in all of those gauge conditions.