Phase transitions in the early universe

TL;DR

This paper reviews the physics of first-order phase transitions in the early universe, their potential gravitational wave signatures, and how future detectors like LISA could observe these signals, shedding light on beyond Standard Model theories.

Contribution

It provides a comprehensive overview of the theoretical framework for early universe phase transitions and their gravitational wave imprints, connecting particle physics with cosmological observations.

Findings

Key quantities of phase transitions are identified and characterized.

The gravitational wave spectrum from phase transitions is linked to observable parameters.

Future space-based detectors like LISA could detect these primordial signals.

Abstract

These lecture notes are based on a course given by Mark Hindmarsh at the 24th Saalburg Summer School 2018 and written up by Marvin L\"uben, Johannes Lumma and Martin Pauly. The aim is to provide the necessary basics to understand first-order phase transitions in the early universe, to outline how they leave imprints in gravitational waves, and advertise how those gravitational waves could be detected in the future. A first-order phase transition at the electroweak scale is a prediction of many theories beyond the Standard Model, and is also motivated as an ingredient of some theories attempting to provide an explanation for the matter-antimatter asymmetry in our Universe. Starting from bosonic and fermionic statistics, we derive Boltzmann's equation and generalise to a fluid of particles with field dependent mass. We introduce the thermal effective potential for the field in its lowest order approximation, discuss the transition to the Higgs phase in the Standard Model and beyond, and compute the probability for the field to cross a potential barrier. After these preliminaries, we provide a hydrodynamical description of first-order phase transitions as it is appropriate for describing the early Universe. We thereby discuss the key quantities characterising a phase transition, and how they are imprinted in the gravitational wave power spectrum that might be detectable by the space-based gravitational wave detector LISA in the 2030s.