Primordial black holes (PBHs) can form in the early Universe via the collapse of large density perturbations. There are tight constraints on the abundance of PBHs formed due to their gravitational effects and the consequences of their evaporation. These abundance constraints can be used to constrain the primordial power spectrum, and hence models of inflation, on scales far smaller than those probed by cosmological observations. We compile, and where relevant update, the constraints on the abundance of PBHs before calculating the constraints on the curvature perturbation, taking into account the growth of density perturbations prior to horizon entry. We consider two simple parametrizations of the curvature perturbation spectrum on the scale of interest: constant and power-law. The constraints from PBHs on the amplitude of the power spectrum are typically in the range $10^{−2}–10^{−1}$ with some scale dependence.
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