Short baseline neutrino experiments such as LSND and MiniBooNE seem to suggest the existence of light sterile neutrinos. Meanwhile, current cosmic microwave background and big bang nucleosynthesis measurements place an upper bound on the effective number of light neutrinos, $N_{\mathrm{eff}}$ and the PLANCK satellite will measure $N_{\mathrm{eff}}$ 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 $N_{\mathrm{eff}}$ inferred from big bang nucleosynthesis and PLANCK. This mechanism can accommodate two eV sterile neutrinos even if PLANCK observes $N_{\mathrm{eff}}$ 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 $N_{\mathrm{eff}}$. 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 cosmic microwave background bound on $N_{\mathrm{eff}}$ if only active neutrinos are considered.

• Received 12 December 2012

DOI:https://doi.org/10.1103/PhysRevD.87.065016