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. First, the action for perturbations about the classical solution has the wrong sign and such perturbations are therefore unsuppressed. Second, with this sign for the action 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