Hidden Sector Relic Abundances from an Effective Planck Mass

Hidden sectors are generic in beyond the Standard Model constructions and string compactifications. We consider models featuring hidden sectors that have dark matter candidates. The relic density is set in part by the energy-injecting inflaton branching ratio B to the sector. We develop a general framework to determine the dependence on B for thermalized hidden sectors by defining an effective Planck mass for the Boltzmann equations for the hidden sector degrees of freedom. We apply this framework to several representative examples, including freeze-out/freeze-in WIMPs and multi-component dark matter. We find that the fractional energy density carried by freeze-out relics (in both single and multi-component models) and monopoles produced from second order phase transitions scale as B 1/4 and thus may lead to an overclosure problem, even with B 1. On the other hand, the energy density of freeze-in relics scales as B 5/4 and is thus cosmologically irrelevant for sufficiently small B. Finally, we discuss the cumulative implications of a large number of hidden sectors.