Non-linear curvature inhomogeneities and backreaction for relativistic viscous fluids

TL;DR

This paper investigates how relativistic viscous fluids influence large-scale curvature inhomogeneities, revealing conditions under which curvature perturbations are prevented from growing non-linearly, with implications for cosmological models.

Contribution

It introduces a symmetry in the evolution equations for curvature inhomogeneities when bulk viscosity depends on energy density, allowing for exact solutions at leading order.

Findings

Bulk viscosity as a function of energy density prevents non-linear growth of curvature perturbations.

Shear viscosity does not influence curvature evolution or acceleration.

Curvature modes are invariant under coordinate transformations in the perturbative regime.

Abstract

The non-perturbative curvature inhomogeneities induced by relativistic viscous fluids are not conserved in the large-scale limit. However when the bulk viscosity is a function of the total energy density of the plasma (or of the trace of the extrinsic curvature) the relevant evolution equations develop a further symmetry preventing the non-linear growth of curvature perturbations. In this situation the fully inhomogeneous evolution can be solved to leading order in the gradient expansion. Over large-scales both the acceleration and the curvature inhomogeneities are determined by the bulk viscosity coefficients. Conversely the shear viscosity does not affect the evolution of the curvature and does not produce any acceleration. The curvature modes analyzed here do not depend on the choice of time hypersurfaces and are invariant for infinitesimal coordinate transformations in the perturbative regime.