## Phase transitions in the early universe

Mark Hindmarsh, Marvin Lüben, Johannes Lumma, Martin Pauly

SciPost Phys. Lect. Notes 24 (2021) · published 15 February 2021

- doi: 10.21468/SciPostPhysLectNotes.24
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### 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.

##### This publication has been updated

- Correction: Phase transitions in the early universe on 2021-04-15

### Cited by 87

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}^{2}^{3}Mark Hindmarsh, -
^{4}Marvin Lüben, -
^{5}Johannes Lumma, -
^{5}Martin Pauly

^{1}Helsingfors universitet / University of Helsinki [UH]^{2}University of Sussex^{3}Helsinki Institute of Physics^{4}Max-Planck-Institut für Physik / Max Planck Institute for Physics [MPP]^{5}Ruprecht-Karls-Universität Heidelberg / Heidelberg University

- Suomen Akatemia / Academy of Finland
- Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG]
- Deutscher Akademischer Austauschdienst / German Academic Exchange Service [DAAD]
- Max-Planck-Gesellschaft zur Förderung der Wissenschaften / Max Planck Society [MPG]
- Science and Technology Facilities Council [STFC]