Testing the Copernican Principle with Hubble Parameter

TL;DR

This paper investigates the scale at which the Copernican Principle holds using Hubble parameter data within Lemaître-Tolman-Bondi void models, highlighting the potential for future observational tests to confirm cosmic homogeneity.

Contribution

It provides a parameter estimation approach for void models using Hubble data and discusses how future observations can test inhomogeneous cosmologies beyond spherical models.

Findings

Hubble data favors a void radius of 2-3 Gpc.

Spherical LTB void models are largely ruled out by current data.

Future observations could definitively test cosmic homogeneity.

Abstract

Using the longitudinal expression of Hubble expansion rate for the general Lema\^itre-Tolman-Bondi (LTB) metric as a function of cosmic time, we examine the scale on which the Copernican Principle holds in the context of a void model. By way of performing parameter estimation on the CGBH void model, we show that the Hubble parameter data favors a void with characteristic radius of 2 ~ 3 Gpc. This brings the void model closer, but not yet enough, to harmony with observational indications given by the background kinetic Sunyaev-Zel'dovich effect and the normalization of near-infrared galaxy luminosity function. However, the test of such void models may ultimately lie in the future detection of the discrepancy between longitudinal and transverse expansion rates, a touchstone of inhomogeneous models. With the proliferation of observational Hubble parameter data and future large-scale structure observation, a definitive test could be performed on the question of cosmic homogeneity. Particularly, the spherical LTB void models have been ruled out, but more general non-spherical inhomogeneities still need to be tested by observation. In this paper, we utilise a spherical void model to provide guidelines into how observational tests may be done with more general models in the future.