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Phase transitions in the early universe

by Mark Hindmarsh, Marvin Lüben, Johannes Lumma, Martin Pauly

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Submission summary

Authors (as registered SciPost users): Marvin Lüben · Martin Pauly
Submission information
Preprint Link:  (pdf)
Date accepted: 2021-02-08
Date submitted: 2021-01-06 18:09
Submitted by: Pauly, Martin
Submitted to: SciPost Physics Lecture Notes
Ontological classification
Academic field: Physics
  • Gravitation, Cosmology and Astroparticle Physics
  • High-Energy Physics - Theory
  • High-Energy Physics - Phenomenology
Approaches: Theoretical, Computational, Phenomenological


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.

List of changes

We have addressed the helpful comments in the report of Referee 2, see the response to that report for more detail.

We have also corrected typos and added citations to other planned space-based detectors at the end of section 8.1. Further, we have extended the discussion of the fitting parameters by adding the new footnote 8 in section 8.2.

Published as SciPost Phys. Lect. Notes 24 (2021)

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