Future Singularities of Isotropic Cosmologies

We show that globally and regularly hyperbolic future geodesically incomplete isotropic universes, except for the standard all-encompassing ‘big crunch’, can accommodate singularities of only one kind, namely, those having a non-integrable Hubble parameter, H. We analyze several examples from recent literature which illustrate this result and show that such behaviour may arise in a number of different ways. We also discuss the existence of new types of lapse singularities in inhomogeneous models, impossible to meet in the isotropic ones.