Avoiding PBH overproduction in inflation model with modified dispersion relation

TL;DR

This paper investigates whether a modified dispersion relation in inflation can resolve the primordial black hole overproduction problem suggested by PTA gravitational wave data, finding it can reduce overproduction to near 2 sigma levels with specific spectral features.

Contribution

It introduces a modified dispersion relation model that produces a broken-power-law spectrum, alleviating PBH overproduction in line with PTA constraints.

Findings

MDR model yields a broken-power-law spectrum reducing overproduction.

The model can lower PBH overproduction to nearly 2 sigma level.

Small negative non-Gaussianity further improves the solution.

Abstract

The Pulsar Timing Array (PTA) data of nano-Hertz gravitational waves released in 2023 implies that if such gravitational waves comes from the scalar perturbation induction at the end of inflation, the accompanied primordial black holes (PBHs) will be over-produced, with the fraction exceed the upper bound of unity. This is recognized as the ``overproduction problem", which calls for nontrivial features in the early universe. In this paper, we try to check out whether a modified dispersion relation (MDR) of the primordial perturbations can be helpful for solving the problem. From the constraint on PTA data, we obtain a posterior distribution of the parameters of primordial perturbation, and find that the MDR model, where the $k^4$ term becomes important at later time, can give rise to a broken-power-law (BPL) power spectrum which can alleviate the overproduction problem to nearly $2\sigma$ level. However, to improve furtherly into $1\sigma$ still needs small negative non-Gaussianity, e.g. $f_{\rm nl}\simeq -1$. The mass distribution of the PBHs generated is also discussed.