Unveiling secret interactions among sterile neutrinos with big-bang nucleosynthesis

Short-baseline neutrino anomalies suggest the existence of low-mass [m similar to O(1) eV] sterile neutrinos upsilon(s). These would be efficiently produced in the early universe by oscillations with active neutrino species, leading to a thermal population of the sterile states seemingly incompatible with cosmological observations. In order to relieve this tension it has been recently speculated that new "secret" interactions among sterile neutrinos, mediated by a massive gauge boson X (with M-X << M-W), can inhibit or suppress the sterile neutrino thermalization, due to the production of a large matter potential term. We note however, that they also generate strong collisional terms in the sterile neutrino sector that induce an efficient sterile neutrino production after a resonance in matter is encountered, increasing their contribution to the number of relativistic particle species N-eff. Moreover, for values of the parameters of the upsilon(s)-upsilon(s) interaction for which the resonance takes place at temperature T less than or similar to few MeV, significant distortions are produced in the electron (anti) neutrino spectra, altering the abundance of light element in big bang nucleosynthesis (BBN). Using the present determination of He-4 and deuterium primordial abundances we determine the BBN constraints on the model parameters. We find that H-2/H density ratio exclude much of the parameter space if one assumes a baryon density at the best fit value of Planck experiment, Omega(B)h(2) = 0.02207, while bounds become weaker for a higher Omega(B)h(2) = 0.02261, the 95% C.L. upper bound of Planck. Due to the large error on its experimental determination, the helium mass fraction Y-p gives no significant bounds.