Equivalent Neutrinos, Light WIMPs, and the Chimera of Dark Radiation

According to conventional wisdom, in the standard model (SM) of particle physics and cosmology the effective number of neutrinos is Neff=3 (more precisely, 3.046). In extensions of the standard model allowing for the presence of DeltaNnu equivalent neutrinos (or dark radiation), Neff is generally >3. The canonical results are reconsidered here, revealing that a measurement of Neff>3 can be consistent with DeltaNnu=0 (dark radiation without dark radiation). Conversely, a measurement consistent with Neff=3 is not inconsistent with the presence of dark radiation (DeltaNnu>0). In particular, if there is a light WIMP that annihilates to photons after the SM neutrinos have decoupled, the photons are heated beyond their usual heating from e+- annihilation, reducing the late time ratio of neutrino and photon temperatures (and number densities), leading to Neff<3. This opens the window for one or more equivalent neutrinos, including sterile neutrinos, to be consistent with Neff=3. By reducing the neutrino number density at present, this allows for more massive neutrinos, relaxing the current constraints on the sum of the neutrino masses. In contrast, if the light WIMP only couples to the SM neutrinos and not to the photons, its late time annihilation heats the neutrinos but not the photons, resulting in Neff>3 even in the absence of equivalent neutrinos or dark radiation. A measurement of Neff>3 is thus no guarantee of the presence of equivalent neutrinos or dark radiation. In the presence of light WIMPs 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 or 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). There's more to a measurement of Neff than meets the eye.