Bounds on light sterile neutrino mass and mixing from cosmology and laboratory searches

We provide a consistent framework to set limits on properties of light sterile neutrinos coupled all three active using combination the latest cosmological data and terrestrial measurements from oscillations, $\beta$-decay neutrinoless double-$\beta$ decay ($0\nu\beta\beta$) experiments. directly constrain full $3+1$ active-sterile mixing matrix elements $|U_{\alpha4}|^2$, with $\alpha \in ( e,\mu ,\tau )$, mass-squared splitting $\Delta m^2_{41} \equiv m_4^2-m_1^2$. find that results for case differ previously studied $1+1$ scenarios where is only one neutrinos, which largely explained by parameter space volume effects. Limits mass are currently dominated sets. The exact slightly prior dependent, but we reliably be constrained below $|U_{\alpha4}|^2 \lesssim 10^{-3}$. Short-baseline neutrino oscillation hints in favor eV-scale serious tension these bounds, irrespective assumptions. also translate bounds analysis into constraints parameters probed laboratory searches, such as $m_\beta$ or $m_{\beta \beta}$, effective $0\nu\beta\beta$ respectively. When allowing neutrino, cosmology leads upper $m_\beta < 0.09$ eV \beta} 0.07$ at 95\% C.L, more stringent than current