A pr 1 99 8 Comment on ‘ Quantum Creation of an Open Universe ’ , by Andrei Linde

We comment on Linde’s claim that one should change the sign in the action for a Euclidean instanton in quantum cosmology, resulting in the formula P ∼ e+S for the probability of various classical universes. There are serious problems with doing so. If one reverses the sign of the action of both the instanton and the fluctuations, the latter are unsupressed and the calculation becomes meaningless. So for a sensible result one would have to reverse the sign of the action for the background, while leaving the sign for the perturbations fixed by the usual Wick rotation. The problem with this approach is that there is no invariant way to split a given four geometry into background plus perturbations. So the prescription would have to violate general coordinate invariance. There are other indications that a sign change is problematic. With the choice P ∼ e+S the nucleation of primordial black holes during inflation is unsuppressed, with a disastrous resulting cosmology. We regard these as compelling arguments for adhering to the usual sign given by the Wick rotation. In a recent letter, we pointed out the existence of new finite action instanton solutions describing the birth of open inflationary universes according to the Hartle-Hawking no boundary proposal. Linde has written a response in which he claims that the Hartle-Hawking calculation of the probability for classical universes is wrong, and that the expresssion