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10. Less-standard ingredients

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 gtapprox 0.05 eV, so that Omeganu gtapprox 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 Omegamh (figure 21). A limit on the neutrino fraction thus requires a prior on Omegamh. Based on the cluster baryon fraction plus BBN, Elgaroy et al. adopt Omegam < 0.5; together with the HST Hubble constant, this yields a marginalized 95% limit of fnu < 0.13, or mnu < 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 mnu < 0.6 eV for any one species. Including the latest WMAP results in order to set a more strict limit on Omegamh, this limit falls to 0.23 eV (Spergel et al. 2003).

Figure 21

Figure 21. Results from Elgaroy et al. (2002), who considered constraints on the neutrino mass from 2dFGRS. The first panel shows Power spectra for Omeganu = 0 (solid line), Omeganu = 0.01 (dashed line), and Omeganu = 0.05 (dot-dashed line) with amplitudes fitted to the 2dFGRS power spectrum data (vertical bars). Other parameters are fixed at Omegam = 0.3, OmegaLambda = 0.7, h = 0.7, Omegab h2 = 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 fnu ident Omeganu / Omegam and Gamma ident Omegam h, with marginalization over h and Omegab h2 using Gaussian priors.

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