# Thermal effect on primordial black holes in standard Higgs minimum double-well potential

## TL;DR

This paper explores how thermal effects influence primordial black hole formation within the Higgs field's double-well potential, using stochastic differential equations and analyzing different perturbation models.

## Contribution

It introduces a novel approach combining Higgs field dynamics with thermal effects via stochastic equations, revealing specific PBH mass distributions and effects of perturbations.

## Key findings

- Primordial black holes dominate at a specific mass range.
- Extremely large or small mass PBHs are nearly excluded.
- Symmetry breaking increases PBH formation probability.

## Abstract

We attempt a new scheme to combine the Higgs field in the minimal standard model and the statistic physics with thermal effect together. By introducing the stochastic differential equation in FRW metric frame which is something like the warm inflation model but not exactly the same. By using the previous researches on Fokker-Planck equation with double-well potential, we find the abundance of primordial black holes (PBHs) dominate at a special mass and the PBHs with extremely large or extremely small mass could be almost excluded. In addition, two perturbed model within this frame are employed, one is the model with symmetry breaking and another is stochastic resonance. The former may increase the probability to the generation of PBHs, while the latter may both increase and decrease the probability. Finally, we also discuss the possibility on extension this scenario to other models.