On the approach to the cosmological singularity in quadratic theories of gravity: The Kasner regimes

Abstract

We study the Kasner-type solutions of the vacuum field equations of D-dimensional theories of gravity which derive from lagrangians that are non-linear in the curvature. We treat both the generic quadratic case which yields field equations of fourth order in the metric and the Lovelock theory whose field equations remain second order. We show that in four-dimensional space-times the standard Kasner solution is always a solution is always a solution (and often the only one) whereas in D > 4 space times all spatial dimensions can always contract as one goes backward in time, contrary to what happens in einsteinian gravity. The bearing of these results on the conjecture that the chaotic approach to the Big Bang singularity is specific to four-dimensional space-times is briefly discussed. © 1989.