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.
