Phase Transitions and Gravitational Wave Tests of Pseudo-Goldstone Dark Matter in the Softly Broken U(1) Scalar Singlet Model

Understand

We study phase transitions in a softly broken $U(1)$ complex singlet scalar model in which the dark matter is the pseudo-scalar part of a singlet whose direct detection coupling to matter is strongly suppressed.

• Our aim is to find ways to test this model with the stochastic gravitational wave background from the scalar phase transition.
• We find that the phase transition which induces vacuum expectation values for both the Higgs boson and the singlet - necessary to provide a realistic dark matter candidate - is always of the second order.
• If the stochastic gravitational wave background characteristic to a first order phase transition will be discovered by interferometers, the soft breaking of $U(1)$ cannot be the explanation to the suppressed dark matter-baryon coupling, providing a conclusive negative test for this class of singlet models.