We use the observational Hubble parameter data (OHD), both the latest observational data set (Stern et al.; referred to as SJVKS) and the simulated data sets, to constrain Lema?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 data set of SN Ia as well as OHD. Despite their different parameterization, the results from our test models show some 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 data set, 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 data set 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 data set keep favoring different voids, in a similar manner as they do at present, the 1σ confidence regions obtained from the two probes should finally separate. We test this conjecture and find that the minimum observational requirement (the size of the data set, the uncertainty level, and the survey depth) for this inconsistency to emerge depends strongly on the void model.
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