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We study pseudo-Goldstone dark matter in the $\mathbb{Z}_{3}$ complex scalarsinglet model. Because the direct detection spin-independent cross section issuppressed, such dark matter is allowed in a large mass range. Unlike in theoriginal model stabilized by a parity, due to the cubic coupling of the singletthe $\mathbb{Z}_{3}$ model can accommodate first-order phase transitions thatgive rise to a stochastic gravitational wave signal potentially observable infuture space-based detectors.

Gravitational Wave Signals of Pseudo-Goldstone Dark Matter in the $\mathbb{Z}_{3}$ Complex Singlet Model