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This is a sequel to a previous detailed study of quantum corrections tocosmological correlations. It was found there that except in special casesthese corrections depend on the whole history of inflation, not just on thebehavior of fields at horizon exit. It is shown here that at least inperturbation theory these corrections can nevertheless not be proportional topositive powers of the Robertson--Walker scale factor, but only at most topowers of its logarithm, and are therefore never large.Comment: 10 pages. Some explanations and references added. Paper now accepted  for publication in Physical Revie

Quantum contributions to cosmological correlations. II. Can these corrections become large?