Subdominant Dark Matter sterile neutrino resonant production in the light of Planck

Few independent detections of a weak X-ray line at an energy of $\sim$3.5 keV seen toward a number of astrophysical sites have been reported. If this signal will be confirmed to be the signature of decaying DM sterile neutrino with a mass of ~7.1 keV, then the cosmological observables should be consistent with its properties. In this paper we make a coupled treatment of the weak decoupling, primordial nucleosynthesis and photon decoupling epochs in the sterile neutrino resonant production scenario, including the extra radiation energy density via N_eff. We compute the radiation and matter perturbations including the full resonance sweep solution for active-sterile flavor conversion in the expanding Universe. We show that the cosmological measurements are in agreement with sub-dominant DM sterile neutrino resonant production with following parameters (errors at 95 CL): sterile neutrino mass 6.08 \pm 3.22 keV, mixing angle \sin^2 2 \theta < 5.61 x 10^{-10}, lepton number per flavor L_4 = 1.23 \pm 0.04 and sterile neutrino mass fraction f_\nu < 0.078. Our results are in good agreement with the sterile neutrino resonant production parameters inferred in Ref. [62] from the linear large scale structure constraints to produce full Dark Matter density.