New isotropic and anisotropic sudden singularities

We show the existence of an infinite family of finite-time singularities in isotropically expanding universes which obey the weak, strong and dominant energy conditions. We show what new type of energy condition is needed to exclude them ab initio. We also determine the conditions under which finite-time future singularities can arise in a wide class of anisotropic cosmological models. New types of finite-time singularity are possible which are characterized by divergences in the time rate of change of the anisotropic-pressure tensor. We investigate the conditions for the formation of finite time singularities in a Bianchi-type VII0 universe with anisotropic pressures and construct specific examples of anisotropic sudden singularities in these universes.