Equivalent neutrinos, light WIMPs, and the chimera of dark radiation

Abstract

According to conventional wisdom, in the standard model (SM) of particle physics and cosmology the ``effective number of neutrinos'' measured in the late Universe is ${N}_{\mathrm{eff}}=3$ (more precisely, 3.046). For extensions of the standard model allowing for the presence of $\ensuremath{\Delta}{N}_{\ensuremath{\nu}}$ ``equivalent neutrinos'' (or ``dark radiation''), it is generally the case that ${N}_{\mathrm{eff}}>3$. These canonical results are reconsidered, demonstrating that a measurement of ${N}_{\mathrm{eff}}>3$ can be consistent with $\ensuremath{\Delta}{N}_{\ensuremath{\nu}}=0$ (``dark radiation without dark radiation''). Conversely, a measurement consistent with ${N}_{\mathrm{eff}}=3$ is not inconsistent with the presence of dark radiation ($\ensuremath{\Delta}{N}_{\ensuremath{\nu}}>0$). In particular, if there is a light weakly interacting massive particle (WIMP) that annihilates to photons after the SM neutrinos have decoupled, the photons are heated beyond their usual heating from ${e}^{\ifmmode\pm\else\textpm\fi{}}$ annihilation, reducing the late time ratio of neutrino and photon temperatures (and number densities), leading to ${N}_{\mathrm{eff}}<3$. This opens the window for one or more equivalent neutrinos, including ``sterile neutrinos,'' to be consistent with ${N}_{\mathrm{eff}}=3$. By reducing the neutrino number density in the present Universe, this also allows for more massive neutrinos, relaxing the current constraints on the sum of the neutrino masses. In contrast, if the light WIMP couples only to the SM neutrinos and not to the photons and ${e}^{\ifmmode\pm\else\textpm\fi{}}$ pairs, its late time annihilation heats the neutrinos but not the photons, resulting in ${N}_{\mathrm{eff}}>3$ even in the absence of equivalent neutrinos or dark radiation. A measurement of ${N}_{\mathrm{eff}}>3$ is no guarantee of the presence of equivalent neutrinos or dark radiation. In the presence of a light WIMP and/or equivalent neutrinos, there are degeneracies among the light WIMP mass and its nature (fermion or boson, as well as its couplings to neutrinos and photons), the number and nature (fermion or boson) of the equivalent neutrinos, and their decoupling temperature (the strength of their interactions with the SM particles). As the analysis here reveals, there's more to a measurement of ${N}_{\mathrm{eff}}$ than meets the eye.