Scalar dark matter production from preheating and structure formation constraints

We investigate the out-of-equilibrium production of scalar dark matter (DM) from inflaton condensate during inflation and reheating. assume that this couples only to via a direct quartic coupling is minimally coupled gravity. consider all possible regimes: purely gravitational, weak (perturbative), strong (non-perturbative). For each regime, we use different approaches determine phase space distribution corresponding relic abundance. gravitational quanta are copiously excited resulting in an infrared (IR) dominated function abundance which overcloses universe for reheating temperature $T_\text{reh}>34 ~\text{GeV}$. A non-vanishing induces effective DM mass suppresses large IR modes favor ultraviolet (UV) minimal generated when interference between couplings maximal. couplings, backreaction on accounted by using Hartree approximation lattice simulation techniques. Since candidates can behave as non-cold matter, estimate impact such species power spectrum derive constraints Lyman-$\alpha$ measurements. find they correspond lower bound $\gtrsim 3\times 10^{-4} \, \rm{eV}$ production, 20 \rm {eV}$ production. discuss implications these results.