Unveiling secret interactions among sterile neutrinos with big-bang
  nucleosynthesis
  Short-baseline neutrino anomalies suggest the existence of low-mass ( m \sim
O(1)~eV) sterile neutrinos \nu_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 \nu_s-\nu_s interaction for which the
resonance takes place at temperature T\lesssim 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 $^4$He and deuterium primordial abundances we determine the
BBN constraints on the model parameters. We find that $^2$H/H density ratio
exclude much of the parameter space if one assume 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.
