Structure formation in an anisotropic universe: Eulerian perturbation theory

TL;DR

This paper develops an Eulerian perturbation theory framework to analyze the growth of cosmological structures in a universe with slight anisotropy, providing analytic solutions for density contrast, power spectrum, and bispectrum.

Contribution

It introduces a novel analytic approach for non-linear perturbations in anisotropic cosmologies, including explicit formulas for power spectrum and bispectrum corrections.

Findings

Power spectrum exhibits quadrupolar anisotropic correction.

Bispectrum shows angle-dependent modifications.

Anisotropic effects peak at a specific redshift between decoupling and today.

Abstract

We present an effective Eulerian description, in the non-relativistic regime, of the growth of cosmological perturbations around a homogeneous but anisotropic Bianchi I spacetime background. We assume a small deviation from isotropy, sourced at late times for example by dark energy anisotropic stress. We thus derive an analytic solution for the linear dark matter density contrast, and use it in a formal perturbative approach which allows us to derive a second order (non-linear) solution. As an application of the procedure followed here we derive analytic expressions for the power spectrum and the bispectrum of the dark matter density contrast. The power spectrum receives a quadrupolar correction as expected, and the bispectrum receives several angle-dependent corrections. Quite generally, we find that the contribution of a late-time phase of anisotropic expansion to the growth of structure peaks at a finite redshift between CMB decoupling and today, tough the exact redshift value is model-dependent.