Upper limits on neutrino masses from the 2dFGRS and WMAP: the role of priors

TL;DR

The study investigates how cosmological data constrain the total neutrino mass, focusing on the 2dFGRS power spectrum and its interplay with priors on $\\omega_m$, $h$, $n$, and $\\omega_b$. It shows that neutrino mass bounds hinge strongly on these priors and the treatment of bias and non-linearities; without a tight matter-density prior, models with sizable neutrino fractions can fit the data, while external priors (notably on $\\omega_m$ and $h$) tighten the limits. The analysis demonstrates that the 2dFGRS data alone cannot yield a non-trivial bound without such priors, and that the WMAP results—especially when combined with Lyman-α data—provide the strongest contemporary constraint, $m_{\\nu,tot} \lesssim 0.7$ eV. Overall, the work emphasizes the critical role of priors and complementary cosmological probes in deriving robust neutrino mass limits from structure formation data.

Abstract

Solar, atmospheric, and reactor neutrino experiments have confirmed neutrino oscillations, implying that neutrinos have non-zero mass, but without pinning down their absolute masses. While it is established that the effect of neutrinos on the evolution of cosmic structure is small, the upper limits derived from large-scale structure data could help significantly to constrain the absolute scale of the neutrino masses. In a recent paper the 2dF Galaxy Redshift Survey (2dFGRS) team provided an upper limit m_nu,tot < 2.2 eV, i.e. approximately 0.7 eV for each of the three neutrino flavours, or phrased in terms of their contributioin to the matter density, Omega_nu/Omega_m < 0.16. Here we discuss this analysis in greater detail, considering issues of assumed 'priors' like the matter density Omega_m and the bias of the galaxy distribution with respect the dark matter distribution. As the suppression of the power spectrum depends on the ratio Omega_nu/Omega_m, we find that the out-of- fashion Mixed Dark Matter Model, with Omega_nu=0.2, Omega_m=1 and no cosmological constant, fits the 2dFGRS power spectrum and the CMB data reasonably well, but only for a Hubble constant H_0<50 km/s/Mpc. As a consequence, excluding low values of the Hubble constant, e.g. with the HST Key Project is important in order to get a strong constraint on the neutrino masses. We also comment on the improved limit by the WMAP team, and point out that the main neutrino signature comes from the 2dFGRS and the Lyman alpha forest.

Figures (12)

• Figure 1: Neutrino mass eigenvalues as functions of their total for the cases of normal (top panel) and inverted (bottom panel) hierarchies. The vertical line marked 'oscillations' is the lower limit derived from the measured mass-squared differences for the two hierarchies. The other vertical lines are upper limits from WMAP+CBI+ACBAR+2dFGRS+Ly $\alpha$, 2dFGRS, and $^3{\rm H}$$\beta$ decay.
• Figure 2: Ratio of the transfer functions for various values of $\Omega_\nu$ to the one for $\Omega_\nu = 0$. The other parameters are fixed at $\Omega_{\rm m}=0.3$, $\Omega_{\rm b}=0.04$, $h=0.7$.
• Figure 3: Ratio of power spectra for $\Omega_\nu =0.01$ (bottom line) and $\Omega_\nu=0.05$ (top line) to the one for $\Omega_\nu = 0$ (horizontal line) with amplitudes fitted to the 2dFGRS power spectrum data (vertical bars) in redshift space. We have fixed $\Omega_{\rm m}=0.3$, $h=0.7$, and $\Omega_{\rm b}h^2 = 0.02$. The vertical dashed lines limit the range in $k$ used in the fits.
• Figure 4: Probability distributions, normalized so that the area under each curve is equal to one, for $f_\nu$ with marginalization over the other parameters, as explained in the text, for $N_\nu =3$ massive neutrinos and $\Omega_{\rm m}h=0.16$ (full line), $0.20$ (dotted line), and $0.24$ (dashed line).
• Figure 5: Confidence contours (68 and 95 %) from the 2dFGRS data alone in the plane of total neutrino mass $m_{\nu,\rm tot}=94\omega_\nu\;{\rm eV}$ and the physical matter density $\omega_{\rm m}$. The bias parameter and $\sigma_8$ have been marginalized over with top-hat priors, $\omega_{\rm b}$, $h$, and $n$ are fixed at their best-fitting values.