Weighing Neutrinos with Galaxy Surveys

Abstract

We show that galaxy redshift surveys sensitively probe the neutrino mass, with eV mass neutrinos suppressing power by a factor of two. The Sloan Digital Sky Survey can potentially detect $N$ nearly degenerate massive neutrino species with mass m_nu > 0.65 (Omega_m h^2/0.1 N)^{0.8} eV at better than 2sigma once microwave background experiments measure two other cosmological parameters. Significant overlap exists between this region and that implied by the LSND experiment, and even m_nu ~ 0.01-0.1 eV, as implied by the atmospheric anomaly, can affect cosmological measurements.

Figures (3)

• Figure 1: Effect of a 1 eV neutrino on the BRG power spectrum compared with expected precision of the SDSS BRG survey (1$\sigma$ error boxes, assuming $\sigma_8=2$ for the BRGs). Upper curves: an $\Omega_m=1.0$, $h=0.5$, $\Omega_b h^2=0.0125$, $n=1$ model with and without a 1 eV neutrino mass. Lower curves: the same but for an $\Omega_m=0.2$, $h=0.65$ model.
• Figure 2: Standard deviation $\sigma({m_\nu})$ as a function of the upper cutoff $k_{\rm max}$ for several different choices of prior cosmological constraints. Models are the same as in Fig. \ref{['fig:neutrino_1']} and have $m_\nu=1{\rm\,eV}$. ( a) High $\Omega_m h^2$: no priors, solid line; single prior of $\sigma(\Omega_m h^2)=0.04$, dashed line; full CMB prior (see text), long-dashed line. ( b) Low $\Omega_m h^2$: as ( a), save that the single prior is $\sigma(n)=0.06$, dashed line.
• Figure 3: The $2\sigma$ detection threshold for $m_\nu$ from the SDSS BRG survey as a function of the matter density $\Omega_m h^2$ for the number of degenerate mass neutrinos $N=1$--3. We have used $h=0.5$, $\Omega_bh^2=0.0125$, $n=1$, and $k_{\rm max}=0.2h{\rm\,Mpc}^{-1}$; variations on these produce only mild shifts.