Dark radiation constraints on portal interactions with hidden sectors

We update dark radiation constraints on millicharged particle (MCP) and gauged baryon-number-minus-lepton-number ($B-L$) extensions of the Standard Model (SM). In these models, a massive SM gauge singlet mediator couples the SM plasma to additional SM-singlet light degrees of freedom. In the early Universe, these new light particles are populated via the interaction of the SM with the MCP, or the new $B-L$ gauge boson, and act as dark radiation. The presence of dark radiation in the early Universe is tightly constrained by current and upcoming cosmic microwave background (CMB) measurements. We update bounds on MCPs from current measurements of $N_{\rm eff}$ and show that future CMB experiments will be able to rule out or discover the extended MCP model invoked to explain the EDGES anomaly. Our analysis of the gauged $B-L$ model goes beyond previous studies by including quantum-statistical and out-of-equilibrium effects. Further, we account for the finite lifetime of the $B-L$ gauge boson, which boosts the subsequent right-handed neutrino energy density. We also develop a number of approximations and techniques for simplifying and solving the relevant Boltzmann equations. We use our approximations to develop a lower bound on the radiation density in a generic hidden sector with a light relic that is insensitive to the details of the hidden sector, provided the mediator interacts more strongly with the hidden sector than with the SM.