Mimicking dark energy with Lemaître-Tolman-Bondi models: Weak central singularities and critical points

There has been much debate over whether or not one could explain the observed acceleration of the Universe with inhomogeneous cosmological models, such as the spherically-symmetric Lema\^tre-Tolman-Bondi (LTB) models. It has been claimed that the central observer in these models can observe a local acceleration, which would contradict general theorems. We resolve the contradiction by noting that many of the models that have been explored contain a weak singularity at the location of the observer which makes them unphysical. In the absence of this singularity, we show that LTB models must have a positive central deceleration parameter q₀, in agreement with the general theorems. We also show that it is possible to achieve a negative apparent deceleration parameter at nonzero redshifts in LTB models that do not contain this singularity. However, we find other singularities that tend to arise in LTB models when attempting to match luminosity distance data, and these generally limit the range of redshifts for which these models can mimic observations of an accelerating Universe. Exceptional models do exist that can extend to arbitrarily large redshift without encountering these pathologies, and we show how these may be constructed. These special models exhibit regions with negative effective equation of state parameter, which may fall below negative one, but we have failed to find any singularity-free models that agree with observations. Moreover, models based on dust-filled LTB metrics probably fail to reproduce observed properties of large scale structure.