Generating large primordial fluctuations in single-field inflation for PBH formation

Abstract

In order to produce appreciable amount of primordial black holes (PBHs), the square amplitude of curvature perturbation must take a large value of $\mathcal{O}(0.01)$, namely, seven digits larger than the value observed by cosmic microwave background radiation (CMB) on large scales. Such a large fluctuation can be achieved by violating the slow-roll (SR) condition within a short duration. The best known of such possibilities is the ultraslow-roll (USR) inflation. We calculate the power spectrum of curvature perturbation in a simple single-field inflation model which evolves through the SR-USR-SR regimes so that both large-amplitude small-scale fluctuation for PBH formation and small-amplitude large-scale fluctuation as observed by CMB are realized. We further calculate the bispectrum and one-loop correction to the power spectrum induced by the third-order action of curvature perturbation as the beginning of precision cosmology on small scales. As a result, we show that single-field inflation model realizing PBH formation can be constrained by the quantum correction.

Invited chapter to the book "Primordial Black Holes'', Springer 2024, ed. Chris Byrnes, Gabriele Franciolini, Tomohiro Harada, Paolo Pani, Misao Sasaki

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