  Short baseline neutrino experiments such as LSND and MiniBooNE seem to
suggest the existence of light sterile neutrinos. Meanwhile, current cosmic
microwave background (CMB) and big bang nucleosynthesis (BBN) measurements
place an upper bound on the effective number of light neutrinos, $N_{eff}$ and
the PLANCK satellite will measure $N_{eff}$ to a much higher accuracy and
further constrain the number of sterile neutrinos allowed. We demonstrate that
if an MeV dark matter particle couples more strongly to electrons and/or
photons than to neutrinos, then p-wave annihilation after neutrino decoupling
can reduce the value of $N_{eff}$ inferred from BBN and PLANCK. This mechanism
can accommodate two eV sterile neutrinos even if PLANCK observes $N_{eff}$ as
low as the standard model theoretical value of 3.046, and a large neutrino
asymmetry is not needed to obtain the correct primordial element abundances.
The dark matter annihilation also weakens the cosmological upper bounds on the
neutrino masses, and we derive a relationship between the change in these
bounds and the corresponding change in $N_{eff}$. Dark matter with an electric
dipole moment or anapole moment is a natural candidate that exhibits the
desired properties for this mechanism. Coincidentally, a dark matter particle
with these properties and lighter than 3 MeV is precisely one that can explain
the 511 keV gamma-ray line observed by INTEGRAL. We show that the addition of
two eV sterile neutrinos allows this kind of dark matter to be lighter than 3
MeV, which is otherwise ruled out by the CMB bound on $N_{eff}$ if only active
neutrinos are considered.
