Connecting between inflation and dark matter in models with gauged Z_3 symmetry

We investigate the possibility of unifying the inflation and dark matter physics in the minimal model for a complex scalar dark matter with gauged Z3 symmetry. The dark local U(1) symmetry is broken spontaneously into the Z3 symmetry by the dark Higgs mechanism. As compared to dark matter models with Z2 parity, the dark matter cubic self-interaction restricts the inflation with non-minimal couplings to take place beyond the pure dark matter direction and plays an important role in the loop corrections for the inflationary predictions as well as determining the correct dark matter relic density. Considering either of 2→2, 3→2 or forbidden channels to be a dominant production mechanism for dark matter, we show the viable parameter space of the model that is consistent with the theoretical and phenomenological constraints combined from inflation and dark matter.