Cosmic microwave background constraints on secret interactions among
  sterile neutrinos
  Secret contact interactions among eV sterile neutrinos, mediated by a massive
gauge boson $X$ (with $M_X \ll M_W$), and characterized by a gauge coupling
$g_X$, have been proposed as a mean to reconcile cosmological observations and
short-baseline laboratory anomalies. We constrain this scenario using the
latest Planck data on Cosmic Microwave Background anisotropies, and
measurements of baryon acoustic oscillations (BAO). We consistently include the
effect of secret interactions on cosmological perturbations, namely the
increased density and pressure fluctuations in the neutrino fluid, and still
find a severe tension between the secret interaction framework and cosmology.
In fact, taking into account neutrino scattering via secret interactions, we
derive our own mass bound on sterile neutrinos and find (at 95% CL) $m_s <
0.82$ eV or $m_s < 0.29$ eV from Planck alone or in combination with BAO,
respectively. These limits confirm the discrepancy with the laboratory
anomalies. Moreover, we constrain, in the limit of contact interaction, the
effective strength $G_X$ to be $ < 2.8 (2.0) \times 10^{10}\,G_F$ from Planck
(Planck+BAO). This result, together with the mass bound, strongly disfavours
the region with $M_X \sim 0.1$ MeV and relatively large coupling $g_X\sim
10^{-1}$, previously indicated as a possible solution to the small scale dark
matter problem.
