M theory model of a big crunch/big bang transition

We consider a picture in which the transition from a big crunch to a big bang corresponds to the collision of two empty orbifold planes approaching each other at a constant nonrelativistic speed in a locally flat background space-time, a situation relevant to recently proposed cosmological models. We show that $p$-brane states which wind around the extra dimension propagate smoothly and unambiguously across the orbifold plane collision. In particular we calculate the quantum mechanical production of winding M2-branes extending from one orbifold to the other. We find that the resulting density is finite and that the resulting gravitational backreaction is small. These winding states, which include the string theory graviton, can be propagated smoothly across the transition using a perturbative expansion in the membrane tension, an expansion which from the point of view of string theory is an expansion in inverse powers of ${\alpha }^{\prime }$. The conventional description of a crunch based on Einstein general relativity, involving Kasner or mixmaster behavior is misleading, we argue, because general relativity is only the leading order approximation to string theory in an expansion in positive powers of ${\alpha }^{\prime }$. In contrast, in the M theory setup we argue that interactions should be well behaved because of the smooth evolution of the fields combined with the fact that the string coupling tends to zero at the crunch. The production of massive Kaluza-Klein states should also be exponentially suppressed for small collision speeds. We contrast this good behavior with that found in previous studies of strings in Lorentzian orbifolds.