Phase transitions in the early universe

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.

Dark holograms and gravitational waves

“…Analogously, the dynamically generated scale, which in the WSS model is denoted as M KK , varies considerably among the various theories, typically from about 100 MeV to about 100 TeV. In this subsection we consider the WSS model with N f flavors, in the regime (2.1), 10 as providing a strongly-correlated large N dark QCD-like sector. Previous studies of gravitational wave spectra in similar scenarios include [33][34][35][36][37][38].…”

“…The bubbles can generate GWs either by their collisions or by their interaction with the plasma medium, through sound waves or turbulence. We refer to [7][8][9][10] for reviews.…”

Gravitational waves from a holographic phase transition

“…where Γ(t)/V is the nucleation rate per unit volume in the symmetric phase. This is evaluated at a time t f which is at the temperature where the nucleation rate averaged over the whole universe peaks, and can be used to define the nucleation temperature [3]. From these quantities the scale of the theory in the form of the typical bubble separation is set by…”

“…If this was a first order transition, gravitational waves would have been produced through bubble nucleation, collision and counter-propagating sound waves (see e.g. [3]). There is a strong possibility that they would be of the right frequency to be observed by a space-based gravitational wave detector such as LISA (Laser Interferometer Space Antenna) [4].…”

Gravitational wave signatures from domain wall and strong first-order phase transitions in a two complex scalar extension of the Standard Model

“…As mentioned, in the non-runaway scenario the production mechanism of GWs from the strong first-order electroweak phase transition are mainly driven by two processes namely sound waves induced by the bubbles running through the cosmic plasma [24][25][26][27] and turbulence induced by the bubble expansions in the cosmic plasma [28][29][30][31][32]. The total GW intensity Ω GW h 2 from the SFOPT for a particular frequency f can be obtained by adding the contributions of the above two mechanisms and we have [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]]…”