Back Reaction And Local Cosmological Expansion Rate

TL;DR

This paper investigates how cosmological perturbations influence the local expansion rate of the universe, finding that infrared effects vanish when using matter fields as clocks, with implications for realistic cosmological models.

Contribution

It provides a detailed analysis of back reaction effects on the local expansion rate in different cosmological scenarios, highlighting the importance of the choice of time variable.

Findings

Infrared back reaction effects vanish when measured at fixed matter field values.

Back reaction effects do not vanish when measured at fixed background time.

Results have implications for understanding the impact of perturbations in realistic cosmological models.

Abstract

We calculate the back reaction of cosmological perturbations on a general relativistic variable which measures the local expansion rate of the Universe. Specifically, we consider a cosmological model in which matter is described by a single field. We analyze back reaction both in a matter dominated Universe and in a phase of scalar field-driven chaotic inflation. In both cases, we find that the leading infrared terms contributing to the back reaction vanish when the local expansion rate is measured at a fixed value of the matter field which is used as a clock, whereas they do not appear to vanish if the expansion rate is evaluated at a fixed value of the background time. We discuss possible implications for more realistic models with a more complicated matter sector.