Is Cosmology Compatible with Sterile Neutrinos?

By combining data from cosmic microwave background experiments (including the recent WMAP third year results), large scale structure, and Lyman-$\alpha$ forest observations, we constrain the hypothesis of a fourth, sterile, massive neutrino. For the $3\mathrm{\text{massless}}+1\mathrm{\text{massive}}$ neutrino case, we bound the mass of the sterile neutrino to $m_s<0.26\mathrm{eV}$ (0.44 eV) at 95% (99.9%) C.L., which excludes at high significance the sterile neutrino hypothesis as an explanation of the LSND anomaly. We generalize the analysis to account for active neutrino masses and the possibility that the sterile abundance is not thermal. In the latter case, the contraints in the $(\mathrm{\text{mass}},\mathrm{\text{density}})$ plane are nontrivial. For a mass of $>1$ or $<0.05\mathrm{eV}$, the cosmological energy density in sterile neutrinos is always constrained to be ${\omega }_{\nu }<0.003$ at 95% C.L., but for a mass of $\sim 0.25\mathrm{eV}$, ${\omega }_{\nu }$ can be as large as 0.01.

Figure 1

The epoch of equality $a_{\mathrm{eq}}$ as a function of mass of a sterile neutrino and its energy density. The nonrelativistic matter density here is fixed to ${\omega }_m=0.15$, so that in the standard 3-neutrino model, $a_{\mathrm{EQ}}=2.82\times {10}^{-4}$. Notice that, at fixed ${\omega }_s$, $a_{\mathrm{eq}}$ rises very rapidly for lower masses since the neutrinos behave as radiation. Thermalized neutrinos lie along the dashed curve.

Figure 2

Effect of an extra sterile neutrino on the CMB (top) and LSS (bottom) power spectra. The thin lines correspond to a standard model, sterile neutrino of mass $m=1\mathrm{eV}$ (dashed line), $m=0.3\mathrm{eV}$ (dotted-dashed line), and fixed sterile density ${\omega }_s=0.01$. These curves are normalized to large scale $C_{\ell }$. The thick dashed and dotted-dashed curves correspond to models which, in addition to having sterile mass, have had dark matter density increased to match standard $a_{\mathrm{eq}}$ and $h$ increased to match CMB peak positions and were normalized at the first peak. The dotted vertical lines in the bottom plot enclose the area where LSS experiments are currently sensitive to, with thick line normalizations chosen to illustrate the fact that the 1 eV model is a poorer fit than 0.3 eV model. See text for discussion.

Figure 3

$1,2\mathrm{\text{−}}\sigma$ constraints on the sterile neutrino mass and abundance.