Dark Radiation from Neutrino Mixing after Big Bang Nucleosynthesis

A light ($m_{\nu d} \lesssim $ MeV) dark fermion mixing with the Standard Model neutrinos can naturally equilibrate with the neutrinos via oscillations and scattering. In the presence of dark sector interactions, production of dark fermions is generically suppressed above BBN, but then enhanced at later times. Over much of the parameter space, we find that the dark sector equilibrates, even for mixing angles $\theta_0$ as small as $10^{-13}$, and equilibration occurs at $T_{\rm equil} \simeq m_{\nu d} \left(\theta_0^2 M_{Pl}/ m_{\nu d} \right)^{1/5} $ which is naturally at most a few orders of magnitude above the dark fermion mass. The implications of this are twofold: one, that light states are often only constrained by the CMB and LSS without leaving an imprint on BBN, and two, that sectors which equilibrate before recombination will typically have a mass threshold before recombination, as well. This can result in dark radiation abruptly transitioning from non-interacting to interacting, or vice-versa, a ``step'' in the amount of dark radiation, and dark matter with similar transitions in its interactions, all of which can leave important signals in the CMB and LSS, and may be relevant for cosmological tensions in observables such as $H_0$ or $S_8$. Minimal models leave an unambiguous imprint on the CMB above the sensitivity of upcoming experiments.Comment: 6 pages, 2 figure