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According to conventional wisdom, in the standard model (SM) of particlephysics and cosmology the effective number of neutrinos is Neff=3 (moreprecisely, 3.046). In extensions of the standard model allowing for thepresence of DeltaNnu equivalent neutrinos (or dark radiation), Neff isgenerally >3. The canonical results are reconsidered here, revealing that ameasurement of Neff>3 can be consistent with DeltaNnu=0 (dark radiation withoutdark radiation). Conversely, a measurement consistent with Neff=3 is notinconsistent with the presence of dark radiation (DeltaNnu>0). In particular,if there is a light WIMP that annihilates to photons after the SM neutrinoshave 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 ormore equivalent neutrinos, including sterile neutrinos, to be consistent withNeff=3. By reducing the neutrino number density at present, this allows formore massive neutrinos, relaxing the current constraints on the sum of theneutrino masses. In contrast, if the light WIMP only couples to the SMneutrinos and not to the photons, its late time annihilation heats theneutrinos but not the photons, resulting in Neff>3 even in the absence ofequivalent neutrinos or dark radiation. A measurement of Neff>3 is thus noguarantee of the presence of equivalent neutrinos or dark radiation. In thepresence of light WIMPs and/or equivalent neutrinos there are degeneraciesamong the light WIMP mass and its nature (fermion or boson, as well as itscouplings to neutrinos or photons), the number and nature (fermion or boson) ofthe equivalent neutrinos, and their decoupling temperature (the strength oftheir interactions with the SM particles). There's more to a measurement ofNeff than meets the eye.

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