Constraints on Lema\^{\i}tre-Tolman-Bondi models from Observational
  Hubble Parameter data
  We use the observational Hubble parameter data (OHD), both the latest
observational dataset (Stern et al. 2010, referred to as SJVKS) and the
simulated datasets, to constrain Lema\^{\i}tre-Tolman-Bondi (LTB) void models.
The necessity of the consistency check on OHD itself in the LTB cosmology is
stressed. Three voids are chosen as test models and are constrained using the
Union2 dataset of SN Ia as well as OHD. Despite their different
parametrization, the results from our test models show some indicating
similarities, e.g., the best-fit voids obtained from OHD are all considerably
broader than those from SN Ia. Due to the small size of the SJVKS dataset, the
constraints are not conclusive. The constraining power of the future OHD
observations are therefore investigated, through a Figure of Merit (FoM)
analysis based on the Monte Carlo simulated data. We found that, in the case
that the future OHD become more consistent with SN Ia, the results from the
test models are almost unanimous: 1) as many as 32 OHD data points at the
SJVKS-like uncertainty level are needed to give a higher FoM than the Union2
dataset of SN Ia; 2) precise observation helps reduce this required number; 3)
increasing the survey depth does not always increase the FoM. On the other
hand, if the future OHD and the Union2 dataset keep favor different voids, in a
similar manner as they do at present, the 1{\sigma} confidence regions obtained
from the two probes should finally separate. We test this conjecture and found
that, the minimum observational requirement (the size of the dataset, the
uncertainty level and the survey depth) for this inconsistency to emerge
depends strongly on the void model.
