Confronting Lemaitre-Tolman-Bondi models with observational cosmology

The possibility that we live in a special place in the universe, close to the centre of a large void, seems an appealing alternative to the prevailing interpretation of the acceleration of the universe in terms of Lambda CDM model with a dominant dark energy component. In this paper we confront the asymptotically flat Lemaitre-Tolman-Bondi (LTB) models with a series of observations, from type Ia supernovae to cosmic microwave background and baryon acoustic oscillations data. We propose two concrete LTB models describing a local void in which the only arbitrary functions are the radial dependence of the matter density Omega M and the Hubble expansion rate H. We find that all observations can be accommodated within 1 sigma, for our models with four or five independent parameters. The best fit models have a chi(2) very close to that of the Lambda CDM model. A general Fortran program for comparing LTB models with cosmological observations, that has been used to make the parameter scan in this paper, has been made public, and can be downloaded at http://www.phys.au.dk/similar to haugboel/software.shtml together with IDL routines for creating the likelihood plots. We perform a simple Bayesian analysis and show that one cannot exclude the hypothesis that we live within a large local void of an otherwise Einstein-de Sitter model.