On Regularization Scheme Dependence of Predictions in Inflationary Cosmology

We show that there exists a large class of regularization schemes for probabilistic predictions in the theory of a self-reproducing inflationary univere, all of which eliminate the apparent dependence on the time reparametrization. However, all these schemes lead to different answers for relative probabilities of finding various types of post-inflationary universes. Besides, all these schemes fail to be reparametrization invariant beyond the range of the inflaton field close to end of inflation boundary. Therefore, we argue that at the current level of understanding, the simple regularization schemes associated with cutoffs at equal time hypersurfaces are as good as the recently proposed more complicated procedures which try to fix the time-reparametrization dependence.