Testing the Copernican principle with the Hubble parameter.

Using the longitudinal expression of Hubble expansion rate for the general Lemaître-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 constrained Garcia-Bellido-Haugbolle void model, we show that the Hubble parameter data favors a void with a 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 nonspherical inhomogeneities still need to be tested by observation. In this paper, we utilize a spherical void model to provide guidelines into how observational tests may be done with more general models in the future. [ABSTRACT FROM AUTHOR]