# Electroweak phase transition in the presence of hypermagnetic field and the generation of gravitational waves

## TL;DR

This paper explores how a large hypermagnetic field influences the electroweak phase transition, potentially making it first-order in some cases, and predicts detectable gravitational waves from this process.

## Contribution

It introduces a model with a varying weak angle under hypermagnetic influence, showing conditions for a first-order transition and calculating resulting gravitational wave signals.

## Key findings

- Hypermagnetic fields can induce a first-order electroweak phase transition.
- Gravitational waves from the transition could be detected by Ultimate-DECIGO.
- Most parameter space results in a crossover, with only tiny regions showing a first-order transition.

## Abstract

We investigate the effects of a large-scale background hypermagnetic field on the electroweak phase transition. We propose a model in which an effective weak angle varies during the electroweak phase transition and upon its use we show that, although for the majority of the parameter space the phase transition is a crossover, there are tiny regions in which the phase transition occurs in two steps and can be first-order. We obtain all of the important quantities characterizing the details of the first-order phase transition, including the latent heat, transition temperature and duration. We then calculate the gravitational wave energy spectrum generated during the first-order part of the electroweak phase transition and find that, for strong enough background hypermagnetic fields, these signals can be detected by the Ultimate-DECIGO interferometer.