Constraints on the curvature power spectrum from primordial black hole evaporation

Abstract: We estimate the maximum allowed amplitude for the power spectrum of the primordial curvature perturbations, ${\cal P_R}(k)$, on all scales from the absence of any detection signals of sub-solar mass black holes. In particular we analyze the constraints on the PBHs and we focus on the low mass limit where the Hawking radiation is expected to significantly influence the big bang observables, considering also different early cosmic histories. We derive the upper bounds for the variance of density perturbations, $\sigma(M)$, for any possible reheating temperature as well as for the cosmological scenario of a scalar condensate domination. We expect our results to have considerable implications for models designed to generate PBHs, especially in the low mass range, and provide additional constraints to a large class of inflationary models.