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 Lüben, 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.
Highlights
8.2 GWs from first-order phase transitions8.3 Comparison with GW observations
We provide a hydrodynamical description of first-order phase transitions as it is appropriate for describing the early Universe
The main points we would like the reader to take away are: that the gravitational wave power spectrum from a first-order phase transition is calculable from a few thermodynamic properties of matter at very high temperatures; that these parameters are computable from an underlying quantum field theory; and that these parameters are measurable by Laser Interferometer Space Antenna (LISA)
Summary
These lecture notes are intended to provide an introduction to the topic of phase transitions in the early universe, focusing on a possible first-order phase transition at temperatures around the scale of electroweak symmetry-breaking, which the universe reached at an age of around 10−11 s. A thorough study of early universe phase transitions, gravitational wave production and detection, requires quite a lot of theoretical apparatus from particle physics and cosmology, which could not be covered in a short lecture course. The main points we would like the reader to take away are: that the gravitational wave power spectrum from a first-order phase transition is calculable from a few thermodynamic properties of matter at very high temperatures; that these parameters are computable from an underlying quantum field theory; and that these parameters are measurable by LISA.
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