Lemaitre-Tolman-Bondi cosmological models, smoothness, and positivity of the central deceleration parameter

We argued in a previous paper [R. A. Vanderveld et al. 2006, arXiv:astro-ph/0602476] that negative deceleration parameters at the center of symmetry in Lemaitre-Tolman-Bondi cosmological models can only occur if the model is not smooth at the origin. Here we demonstrate explicitly the connection between non-smoothness and the failure of positivity theorems for deceleration. We also address some confusion that has arisen in the literature and respond to some recent criticisms of our arguments.