Gamma-Rays and Gravitational Waves from Inelastic Higgs Portal Dark Matter

We explore a simple and predictive dark matter scenario involving a complex scalar field, $\phi$, coupled to the Higgs portal with no additional field content. In the UV, the field possesses a global $U(1)$ symmetry which is broken by mass terms and Higgs portal interactions. In the mass basis, the complex field splits into a pair of real scalars with a small mass splitting (in analogy to pseudo-Dirac fermions), such that the Higgs portal acquires both diagonal and off-diagonal terms with respect to these eigenstates. In the parameter space where the off-diagonal interaction predominates, this scenario is safe from direct detection constraints. Moreover, this model provides a viable explanation for the longstanding Galactic Center gamma-ray excess. Additionally, this model influences the Higgs potential in a way that could facilitate a strong first-order electroweak phase transition in the early universe, potentially leading to a stochastic gravitational wave background that could fall within the reach of upcoming space-based detectors.