Pole inflation and primordial black holes formation in Starobinsky-like supergravity

TL;DR

This paper extends a supergravity inflation model to produce primordial black holes, finding that a quadratic holomorphic function enables black hole formation consistent with CMB data, but these black holes are too small to account for dark matter.

Contribution

The study introduces a new supergravity model with specific holomorphic functions that can generate primordial black holes during inflation.

Findings

Primordial black holes are produced efficiently only with quadratic holomorphic functions.

The black holes formed are below the Hawking evaporation limit.

Inflation remains viable with the proposed superpotentials.

Abstract

We extend the Cecotti-Kallosh model of Starobinsky inflation in supergravity by adding a holomorphic function to the superpotential in order to generate a large peak in the power spectrum of scalar (curvature) perturbations. In our approach, the singular non-canonical kinetic terms are largely responsible for inflation (as an attractor solution), whereas the superpotential is engineered to generate a production of primordial black holes. We study the cases with (i) a linear holomorphic function, (ii) a quadratic holomorphic function, and (iii) an exponential holomorphic function, as regards the dependence of inflation and primordial black holes production upon parameters of those functions and initial conditions, as well as verify viability of inflation with our superpotentials. We find that an efficient production of primordial black holes consistent with CMB measurements is only possible in the second (ii) case. We calculate the masses of the produced primordial black holes and find that they are below the Hawking (black hole) evaporation limit, so that they cannot be part of the current dark matter in our Universe.