BBN And The CMB Constrain Light, Electromagnetically Coupled WIMPs

In the presence of a light weakly interacting massive particle (WIMP; ${m}_{\ensuremath{\chi}}\ensuremath{\lesssim}30\text{ }\text{ }\mathrm{MeV}$), there are degeneracies among the nature of the WIMP (fermion or boson), its couplings to the standard-model particles (electromagnetic or to neutrinos only), the WIMP mass ${m}_{\ensuremath{\chi}}$, and the number of equivalent neutrinos beyond the standard model $\mathrm{\ensuremath{\Delta}}{\mathrm{N}}_{\ensuremath{\nu}}$ (including possible sterile neutrinos). These degeneracies cannot be broken by the cosmic microwave background (CMB) constraint on the effective number of neutrinos, ${\mathrm{N}}_{\text{eff}}$. However, big bang nucleosynthesis (BBN) is affected by the presence of a light WIMP and equivalent neutrinos, so the combination of BBN and CMB constraints can help to break some of these degeneracies. Here, the BBN predictions for the primordial abundances of deuterium and $^{4}\mathrm{He}$ (along with $^{3}\mathrm{He}$ and $^{7}\mathrm{Li}$) in the presence of a light WIMP and equivalent neutrinos are explored, and the most recent estimates of their observationally determined relic abundances are used to limit the light-WIMP mass, the number of equivalent neutrinos, and the present Universe baryon density (${\mathrm{\ensuremath{\Omega}}}_{\mathrm{B}}{h}^{2}$). These constraints are explored here for Majorana and Dirac fermion WIMPs, as well as for real and complex scalar WIMPs that couple to electrons, positrons, and photons. In a separate paper, this analysis is repeated for WIMPs that couple only to the standard-model neutrinos, and the constraints for the two cases are contrasted. In the absence of a light WIMP, but allowing for $\mathrm{\ensuremath{\Delta}}{\mathrm{N}}_{\ensuremath{\nu}}$ equivalent neutrinos, the combined BBN and CMB constraints favor ${\mathrm{N}}_{\text{eff}}=3.46\ifmmode\pm\else\textpm\fi{}0.17$, ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{B}}{h}^{2}=0.0224\ifmmode\pm\else\textpm\fi{}0.0003$, and $\mathrm{\ensuremath{\Delta}}{\mathrm{N}}_{\ensuremath{\nu}}=0.40\ifmmode\pm\else\textpm\fi{}0.17$ (all at a 68% C.L.). In this case, standard BBN ($\mathrm{\ensuremath{\Delta}}{\mathrm{N}}_{\ensuremath{\nu}}=0$) is disfavored at $\ensuremath{\sim}98%$ confidence, and the presence of one sterile neutrino ($\mathrm{\ensuremath{\Delta}}{\mathrm{N}}_{\ensuremath{\nu}}=1$) is disfavored at $\ensuremath{\gtrsim}99%$ confidence. Allowing for a light WIMP and $\mathrm{\ensuremath{\Delta}}{\mathrm{N}}_{\ensuremath{\nu}}$ equivalent neutrinos together, the combined BBN and CMB data provide lower limits to the WIMP masses (${m}_{\ensuremath{\chi}}\ensuremath{\gtrsim}0.5\ensuremath{-}5\text{ }\text{ }\mathrm{MeV}$) that depend on the nature of the WIMP, favor ${m}_{\ensuremath{\chi}}\ensuremath{\sim}8\text{ }\text{ }\mathrm{MeV}$ (with small variations depending on the WIMP type) slightly over standard BBN, and loosen the constraints on the allowed number of equivalent neutrinos, $\mathrm{\ensuremath{\Delta}}{\mathrm{N}}_{\ensuremath{\nu}}=0.6{5}_{\ensuremath{-}0.35}^{+0.46}$. As a result, while $\mathrm{\ensuremath{\Delta}}{\mathrm{N}}_{\ensuremath{\nu}}=0$ is still disfavored at $\ensuremath{\sim}95%$ confidence when there is a light WIMP, $\mathrm{\ensuremath{\Delta}}{\mathrm{N}}_{\ensuremath{\nu}}=1$ is now allowed.