Late time solutions for inhomogeneous Lambda-CDM cosmology, their characterization and observation

TL;DR

This paper develops a late-time inhomogeneous and anisotropic Lambda-CDM cosmological model, extending standard homogeneous models, and proposes methods to observationally constrain inhomogeneity and anisotropy using luminosity distance measurements.

Contribution

It derives the general inhomogeneous anisotropic Lambda-CDM solution as a late-time expansion, enabling observational constraints on inhomogeneity and anisotropy.

Findings

Derived the inhomogeneous anisotropic Lambda-CDM solution using a series expansion.

Connected the solution to observable luminosity distance-redshift relation.

Suggested geometric flows for averaging inhomogeneous data.

Abstract

Assuming homogeneous isotropic Lambda-CDM cosmology allows Lambda, spatial curvature and dark matter density to be inferred from large scale structure observations such as supernovae. The purpose of this paper is to extend this to allow observations to measure or constrain inhomogeneity and anisotropy. We obtain the general inhomogeneous anisotropic Lambda-CDM solution which is locally asymptotic to an expanding de Sitter solution as a late time expansion using Starobinsky's method (analogous to the `holographic renormalization' technique in AdS/CFT) together with a resummation of the series. The dark matter is modeled as perfect dust fluid. The terms in the expansion systematically describe inhomogeneous and anisotropic deformations of an expanding FLRW solution, and are given as a spatial derivative expansion in terms of data characterizing the solution - a 3-metric and a perturbation of that 3-metric. Leading terms describe inhomogeneity and anisotropy on the scale set by the cosmological constant, approximately the horizon scale today. Higher terms in the expansion describe shorter scale variations. We compute the luminosity distance-redshift relation and argue that comparison with current and future observation would allow a partial reconstruction of the characterizing data. We also comment on smoothing these solutions noting that geometric flows (such as Ricci flow) applied to the characterizing data provide a canonical averaging method.