BBN And The CMB Constrain Neutrino Coupled Light WIMPs

(abridged) In the presence of a light WIMP (mass m_chi < 30 MeV), there are degeneracies among the WIMP's nature, its couplings to standard model particles, its mass, and the number of equivalent (additional) neutrinos, Delta N_nu. These degeneracies cannot be broken by the CMB constraint on the effective number of neutrinos, N_eff. However, since big bang nucleosynthesis (BBN) is also affected by a light WIMP and equivalent neutrinos, complementary BBN and CMB constraints can break some of the degeneracy. In a previous paper BBN and CMB were combined to explore allowed ranges for m_chi, Delta N_nu, and N_eff for light WIMPs that annihilate electromagnetically (EM) to photons and/or electrons/positrons. In this paper BBN predictions with a light WIMP that only couples to neutrinos are calculated. Recent observed abundances of ^2H and ^4He are used to limit m_chi, Delta N_nu, N_eff, and the present-day baryon density. Allowing for a neutrino coupled light WIMP and nonzero Delta N_nu, combined BBN and CMB data give lower limits to m_chi, with a best fit m_chi > 35 MeV, equivalent to no light WIMP at all. All masses below 4--9 MeV (depending on spin) are excluded. Without any light WIMP, BBN alone prefers Delta N_nu = 0.50 +- 0.23, favoring neither Delta N_nu = 0, nor a fully thermalized sterile neutrino (Delta N_nu = 1). This result is consistent with the CMB constraint, N_eff = 3.30 +- 0.27, limiting "new physics" between BBN and recombination. Combining BBN and CMB data gives Delta N_nu = 0.35 +- 0.16 and N_eff = 3.40 +- 0.16; while BBN and the CMB combined require Delta N_nu > 0 at ~98% confidence, they disfavor Delta N_nu > 1 at > 99% confidence. Allowing a neutrino-coupled light WIMP extends the allowed range slightly downward for Delta N_nu and slightly upward for N_eff simultaneously, leaving best-fit values unchanged.