Torsion and the probability of inflation

Abstract

We revisit the problem of the “probability of inflation” from the point of view of the Einstein-Cartan theory, where torsion can be present off-shell even in the absence of spinorial currents. An informal estimate suggests that the barrier for tunneling from “nothing” into a classical universe becomes thinner and lower, should torsion be present, even if only off-shell. We perform a detailed calculation that supports this informal estimate for the case of torsion eigenstates. Finally, we impose a quantum mechanical analog of the zero-torsion condition by restricting to states for which the expectation value of the torsion vanishes. An explicit family of such states is obtained by building wave-packets from linear superpositions of torsion eigenstates with Gaussian weights centered around zero torsion. The tunneling probability for these wave packets is maximized when the variance of the torsion goes to zero. Hence, by considering these wave-packets as the physical states, we recover a sensible model of quantum cosmology that incorporates quantum fluctuations in the torsion, despite the apparently unacceptable conclusions one draws from naïvely considering the tunneling probabilities for the torsion eigenstates.