Backreaction: Gauge and Frame Dependences

TL;DR

This paper investigates how the cosmological backreaction from perturbations depends on gauge and frame choices, highlighting significant dependencies and divergences, and explores specific gauges where backreaction effects are minimized or calculable.

Contribution

It demonstrates the strong gauge- and frame-dependence of backreaction calculations and advocates for volume-preserving gauges, providing explicit examples and analyzing their implications.

Findings

Backreaction exhibits strong gauge- and frame-dependence.

In traceless uniform CDM gauge, backreaction shows ultra-violet divergence.

In uniform curvature gauge, backreaction can vanish or be quantified depending on Hubble rate choice.

Abstract

The cosmological backreaction from perturbations is clearly gauge-dependent, and obviously depends on the choice of averaged Hubble rate. We consider two common choices of Hubble rate and advocate the use of comoving volume-preserving gauges. We highlight two examples valid to an appropriate order in perturbation theory, uniform curvature gauge, which is as close to volume-preserving as possible, and a spatially-traceless uniform cold dark matter gauge which preserves the volume to linear order. We demonstrate the strong gauge- and frame-dependences in averaging. In traceless uniform CDM gauge the backreaction exhibits a strong ultra-violet divergence and can be tuned to an arbitrary magnitude with an appropriate choice of smoothing scale. In uniform curvature gauge we find that for a choice of Hubble rate locked to the spatial surface the backreaction vanishes identically, while for a Hubble rate defined from a fluid's expansion scalar the effective energy density at the current epoch in an Einstein-de Sitter universe is Omega_eff~5e-4, slightly bigger than but in broad agreement with previous results in conformal Newtonian gauge.