By way of expressing the Hubble expansion rate for the general Lemaître-Tolman-Bondi ( LTB ) metric as a function of cosmic time , we test the scale on which the Copernican Principle holds in the context of a void model .
By performing parameter estimation on the CGBH void model , we show the Hubble parameter data favors a void with characteristic radius of 2 \sim 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 .