MG13 Proceedings: A lattice Universe as a toy-model for inhomogeneous cosmology

TL;DR

This paper presents an approximate solution to Einstein's equations modeling a lattice universe with inhomogeneous small scales and homogeneous large scales, highlighting potential discrepancies in cosmological observations.

Contribution

It introduces a new approximate lattice universe model that mimics inhomogeneous cosmology and explores its observational implications.

Findings

Lattice universe expands or contracts like a Friedmann universe with the same average density.

Potential fitting problem between observed and smoothed cosmological models.

Model captures inhomogeneity effects at small scales while maintaining large-scale homogeneity.

Abstract

We briefly report on a previously found new, approximate, solution to Einstein field equations, describing a cubic lattice of spherical masses. This model mimics in a satisfactory way a Universe which can be strongly inhomogeneous at small scales, but quite homogeneous at large ones. As a consequence of field equations, the lattice Universe is found to expand or contract in the same way as the solution of a Friedmann Universe filled with dust having the same average density. The study of observables indicates however the possible existence of a fitting problem, i.e. the fact that the Friedmann model obtained from past-lightcone observables does not match with the one obtained by smoothing the matter content of the Universe.