Testing the Copernican Principle with Hubble Parameter
  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.
