The stability of general relativistic cosmological theory

The authors analyse the behaviour of homogeneous and isotropic solutions to a gravity theory that arises from the variation of an arbitrary analytic function of the space-time scalar curvature. Such a theory generalises Einstein's general relativity wherein this function is linear in the curvature. They prove conditions for the existence and stability of the general relativistic de Sitter and Friedmann solutions within the general theory, prove necessary and sufficient conditions for the existence of cosmological singularities and particle horizons and analyse the asymptotic behaviour of ever-expanding Universe models. The conditions under which Minkowski space-time and Schwarzschild space-time are stable is investigated and their instability, together with the pathological behaviour of certain cosmological models, traced back to the non-minimality of the stationary action giving rise to the field equations. The significance of these results for quantum theories of gravity and the 'inflationary' model of the early Universe is discussed.