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