Density Perturbations and Black Hole Formation in Hybrid Inflation

TL;DR

The paper investigates density perturbations and primordial black hole formation in hybrid inflation models with two inflationary stages, highlighting that the phase transition can generate large perturbations via two-field dynamics and inflating topological defects. It introduces a novel two-field deltaN and stochastic inflation framework to quantify the end-of-inflation perturbations and BH production across parameter space. The results show that, for generic parameters, substantial BH production is expected, but specific model variants (short second stage, large H, or natural hybrid inflation with a pseudo-Goldstone ψ) can avoid problems or even exploit PBHs for dark matter or reheating. The multi-field perturbation approach provides a broadly applicable tool for density perturbation analysis in inflationary models.

Abstract

We investigate the recently proposed hybrid inflation models with two stages of inflation. We show that quantum fluctuations at the time corresponding to the phase transition between the two inflationary stages can trigger the formation of a large number of inflating topological defects. In order to study density perturbations in these models we develop a new method to calculate density perturbations in a system of two scalar fields. We show that density perturbations in hybrid inflation models of the new type can be very large on the scale corresponding to the phase transition. The resulting density inhomogeneities lead to a copious production of black holes. This could be an argument against hybrid inflation models with two stages of inflation. However, we find a class of models where this problem can be easily avoided. The number of black holes produced in these models can be made extremely small, but in general it could be sufficiently large to have important cosmological and astrophysical implications. In particular, for certain values of parameters these black holes may constitute the dark matter in the universe. It is also possible to have hybrid models with two stages of inflation where the black hole production is not suppressed, but where the typical masses of the black holes are very small. Such models lead to a completely different thermal history of the universe, where post-inflationary reheating occurs via black hole evaporation.