Gravitational waves from dark sector phase transitions

The observation of gravitational waves (GWs) promises a new avenue to study fundamental
physics through processes that occurred in the early universe shortly after inflation.
Such observations might provide insights into open questions in our description of the
universe, including the nature of dark matter. In this thesis, we study the phenomenon of
cosmological first-order phase transitions in dark sectors in light of the observation of
a stochastic gravitational wave signal at nanohertz frequencies by the pulsar timing array
(PTA) collaborations.

First, we present the numerical code TransitionListener, which allows the
computation of first-order phase transitions and the resulting gravitational wave spectra
for general models that exhibit spontaneous symmetry breaking. It implements the necessary
computational steps from the construction of the effective potential to the evaluation of
the GW signals and their detectability with current and future experiments.

Using this tool, we study the generic requirements for first-order phase transitions in
dark sectors to explain the observed PTA signal. We investigate three representative model
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classes: an Abelian dark Higgs model, a two-step phase transition with two scalar singlets
and a loop-induced symmetry breaking of a near conformal scalar field. We investigate
their general prediction and discuss the tuning of model parameters needed to achieve a
strong enough phase transition to explain the PTA data. While all considered models can
describe the PTA signal, we find that only the conformal model can do so generically
without significant tuning of the model parameters.

Finally, we explore whether such a dark sector phase transition can simultaneously
generate the mass of a dark matter candidate. We extend the near conformal model,
consisting of a dark Higgs and dark photon, by including a stable fermion as a dark matter
candidate. Since the PTA data requires a phase transition at MeV temperatures, the
spontaneous symmetry breaking gives rise to sub-GeV masses. The dark sector couples to the
Standard Model (SM) through kinetic mixing of the dark and SM photon, enabling the dark
matter candidate to obtains its relic abundance via thermal freeze-out, which proceeds
through annihilations into dark Higgs bosons and electrons. This scenario is subject to
strong constraints from dark photon searches at collider experiments and cosmological
bounds on the decays of the dark Higgs bosons. We perform global fits and identify viable
parameter space, where the model can explain the PTA signal, produce the observed DM relic
abundance and satisfies all relevant cosmological, astrophysical and laboratory
constraints.