RESUMO
The most widely studied formation mechanism of a primordial black hole 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 a model with sharp transition of the second slow-roll parameter. We find that models producing an appreciable amount of primordial black holes induce nonperturbative coupling on a large scale probed by cosmic microwave background radiation. Our result implies that a small-scale power spectrum can be constrained by large-scale cosmological observations.
RESUMO
One-loop correction to the power spectrum in generic single-field inflation is calculated by using standard perturbation theory. Because of the enhancement inversely proportional to the observed red tilt of the spectral index of curvature perturbation, the correction turns out to be much larger than previously anticipated. As a result, the primordial non-Gaussianity must be much smaller than the current observational bound in order to warrant the validity of cosmological perturbation theory.