Cosmological constraints with self-interacting sterile neutrinos

In this work we revisit the question of whether Cosmology can be made compatible with scenarios with light sterile neutrinos, as invoked to explain the SBL anomalies, in the presence of self-interaction among sterile neutrinos mediated by massive gauge bosons. We examine this proposal by deriving the cosmological predictions of the model in a wide range of the model parameters including the effective interaction strength $G_X$, sterile neutrino mass $m_{\rm st}$ and active-sterile mixings. With those we perform a statistical analysis of the cosmological data from BBN, CMB, and BAO data to infer the posterior probabilities of the sterile self-interaction model parameters. BBN mostly provides information about the effective interaction strength and we find that $\log_{10}(G_X/G_F)\geq 3.6$ can describe the primordial abundances at 95% CL. Our analysis of CMB and BAO data show that when allowing a wide prior for the sterile neutrino mass its posterior is bounded to $m_{\rm st}\leq 0.91~{\rm eV}$ (95% CL) considering CMB data only and $m_{\rm st}\leq 0.37~{\rm eV}$ (95% CL) when adding the BAO information. So the mass bounds are slighly relaxed compared with that of a non-interacting sterile neutrino model but a sterile neutrino mass of 1 eV is still excluded at more than $2\sigma$ CL. Conversely if fixing the sterile neutrino mass and mixing to the values prefered by short baseline data we find that while that CMB data alone favors the self-interacting scenario, including the BAO information severly degrades the agreement with the model. Altogether we conclude then that adding the self-interaction can alleviate the tension between eV sterile neutrinos and CMB data, but when including also the BAO results the self-interacting sterile neutrino model cannot lead to a satisfactory description of the data.