The most widely studied formation mechanism of a primordial black hole (PBH)
is collapse of large-amplitude perturbation on small scales generated in
single-field inflation. In this Letter, we calculate one-loop correction to the
large-scale power spectrum in such a model. We find models producing
appreciable amount of PBHs generically induce too large one-loop correction on
large scale probed by cosmic microwave background radiation. We therefore
conclude that PBH formation from single-field inflation is ruled out.
Subjects: High Energy Physics - Theory; Astrophysics - Cosmology and Nongalactic Astrophysics