Constraints on Lemaître-Tolman-Bondi Models From Observational Hubble Parameter Data

Abstract

We use the observational Hubble parameter data (OHD), both the latest observational dataset (Stern et al. (2010a), referred to as SJVKS) and the simulated datasets, to constrain Lemaître-TolmanBondi (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 1σ 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.

Testing the Copernican principle with the Hubble parameter

“…(2), the longitudinal expansion rate H turns out to have the same form as Eq. (4) H = −[1/(1 + z)](dz/dt ct ), and hence corresponds to the observed H(z) [10]. For a general LTB model, the bang time function t B (r) should not be zero, hence the age of the Universe is: T = t − t B (r) so we have dT /dz = (dt/dz) − (dt B /dr)(dr/dz).…”

“…For a general LTB model, the bang time function t B (r) should not be zero, hence the age of the Universe is: T = t − t B (r) so we have dT /dz = (dt/dz) − (dt B /dr)(dr/dz). But as emphasized in our previous paper [10], the gradients (dt B /dr) in the bang time, t B , correspond to a currently non-vanishing decaying mode (also see: [22,24]. This would imply a very inhomogeneous early universe, and hence violate inflation.…”

“…[9,10] for more detailed treatments). Expressed as two functions, Ω m and H ⊥0 , these boundary conditions define an LTB void model.…”

“…[10], because the background in LTB models has considerable inhomogeneities. However, we argue that OHD is still valid in our context (see Discussion).…”

“…In the following we will use the latest 23 data entries as listed in Refs. [15,17], where the data sample is larger than that of 11 OHD used in our previous paper [10].…”