Additional Light Sterile Neutrinos and Cosmology
  Tantalizing cosmological and terrestrial evidence suggests the number of
light neutrinos may be greater than 3, motivating a careful re-examination of
cosmological bounds on extra light species. Big Bang Nucleosynthesis constrains
the number of relativistic neutrino species present during nucleosynthesis,
$N_{eff}^{BBN}$, while measurements of the CMB angular power spectrum constrain
the effective energy density in relativistic neutrinos at the time of
matter-radiation equality, $N_{eff}^{CMB}$. There are a number of scenarios
where new sterile neutrino species may have different contributions to $\Delta
N_{eff}^{BBN}$ and $\Delta N_{eff}^{CMB}$, for masses that may be relevant to
reconciling cosmological constraints with various terrestrial claims of
neutrino oscillations. We consider a scenario with two sterile neutrinos and
explore whether partial thermalization of the sterile states can ease the
tension between cosmological constraints on $N_{eff}^{BBN}$ and terrestrial
data. We then investigate the effect of a non-zero neutrino mass on their
contribution to the radiation abundance, finding reductions in $\Delta
N_{eff}^{CMB}$ of more than 5% for neutrinos with masses above 0.5 eV. While
the effects we investigate here could play a role, we nevertheless find that
two additional light sterile neutrinos species cannot fit all the data at the
95% confidence level.
