No new cosmological concordance with massive sterile neutrinos
  It has been claimed recently that massive sterile neutrinos could bring about
a new concordance between observations of the cosmic microwave background
(CMB), the large-scale structure (LSS) of the Universe, and local measurements
of the Hubble constant, $H_0$. We demonstrate that this apparent concordance
results from combining datasets which are in significant tension, even within
this extended model, possibly indicating remaining systematic biases in the
measurements. We further show that this tension remains when the cosmological
model is further extended to include significant tensor modes, as suggested by
the recent BICEP2 results. Using the Bayesian evidence, we show that the
minimal $\Lambda$CDM model is strongly favoured over its neutrino extensions by
various combinations of datasets. Robust data combinations yield stringent
limits of $\sum m_\nu\lesssim0.3$ eV and $m_{\nu,{\rm sterile}}^{\rm eff}
\lesssim 0.3$ eV at $95\%$ CL for the sum of active and sterile neutrinos,
respectively.
