Interplay between Higgs inflation and dark matter models with dark $U(1)$ gauge symmetry

We investigate dark matter phenomenology and Higgs inflation in a dark $U(1)_D$-extended model. The model features two dark matter candidates, a dark fermion and a dark vector boson. When the fermion dark matter $\psi$ is heavier than the vector dark matter $W_D$, there is an ample parameter space where $\psi$ is dominant over $W_D$. The model can then easily evade the stringent bounds from direct detection experiments, since $\psi$ has no direct coupling to the Standard Model particles. Furthermore, the model can accommodate inflation in three different ways, one along the Standard Model Higgs direction, one along the dark Higgs direction, and one along the combination of the two. Considering the running of the parameters and various observational constraints, we perform a detailed numerical analysis and identify allowed parameter spaces that explain both dark matter and Higgs inflation in a unified manner. We discuss in detail how the imposition of Higgs inflation severely constrains the dark matter parameter space. The existence of the dark Higgs field is found to play a crucial role both in dark matter phenomenology and in generalised Higgs inflation.