10.1. Limits to the neutrino mass
Even though a CDM-dominated universe matches the data very well, there are many plausible variations to consider. Probably the most interesting is the neutrino mass: experimental data on neutrino oscillations mean that at least one neutrino must have a mass of 0.05 eV, so that _{} 10^{-3} - the same order of magnitude as stellar mass.
As explained in earlier, a non-zero neutrino mass can lead to relatively enhanced large-scale power, beyond the neutrino free-streaming scale. This is illustrated in figure 21, taken from Elgaroy et al. (2002). Broadly speaking, allowing a significant neutrino mass changes the spectrum in a way that resembles lower density, so there is a near-degeneracy between neutrino mass fraction and _{m}h (figure 21). A limit on the neutrino fraction thus requires a prior on _{m}h. Based on the cluster baryon fraction plus BBN, Elgaroy et al. adopt _{m} < 0.5; together with the HST Hubble constant, this yields a marginalized 95% limit of f_{} < 0.13, or m_{} < 1.8 eV. Note that this is the sum of the eigenvalues of the mass matrix: given neutrino oscillation results (e.g. Ahmad et al. 2002; Eguchi et al. 2003), the only way a cosmologically significant density can arise is via a nearly degenerate hierarchy, so this allows us to deduce m_{} < 0.6 eV for any one species. Including the latest WMAP results in order to set a more strict limit on _{m}h, this limit falls to 0.23 eV (Spergel et al. 2003).
Figure 21. Results from Elgaroy et al. (2002), who considered constraints on the neutrino mass from 2dFGRS. The first panel shows Power spectra for _{} = 0 (solid line), _{} = 0.01 (dashed line), and _{} = 0.05 (dot-dashed line) with amplitudes fitted to the 2dFGRS power spectrum data (vertical bars). Other parameters are fixed at _{m} = 0.3, _{} = 0.7, h = 0.7, _{b} h^{2} = 0.02. The vertical dashed lines limit the range in k used in the fits. The second panel shows 68% (solid line), 95% (dashed line) and 99% (dotted line) confidence contours in the plane of f_{} _{} / _{m} and _{m} h, with marginalization over h and _{b} h^{2} using Gaussian priors. |