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

Abstract

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 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 ν,tot < 2.2 eV , i.e. approximately 0.7 eV for each of the three neutrino flavours, or phrased in terms of their contribution to the matter density, Ω ν /Ω m < 0.16. Here we discuss this analysis in greater detail, considering issues of assumed 'priors' like the matter density Ω m and the bias of the galaxy distribution with respect to the dark matter distribution. As the suppression of the power spectrum depends on the ratio Ω ν /Ω m , we find that the out-of-fashion Mixed Dark Matter model, with Ω ν = 0.2, Ω m = 1 and no cosmological constant, fits both the 2dFGRS power spectrum and the CMB data reasonably well, but only for a Hubble constant H 0 < 50 km s −1 Mpc −1 . 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 upper limit on the neutrino masses. We also comment on the improved limit obtained by the WMAP team, and point out that the main neutrino signature comes from the 2dFGRS and the Lyman α forest.PACS numbers: 95.35.+d, 14.60.Pq, 98.62.Py, 98.80.Es Upper limits on neutrino masses from the 2dFGRS and WMAP: the role of priors 2

Neutrino oscillations and the early universe

“…Still, the precise analysis of the recent microwave background anisotropy data and structure data at large red-shifts imply the necessity of some admixture of hot DM which can be naturally provided by light neutrinos with Σm ν f < 2.2 eV or m ν f < 0.73 eV (see for example [29,30]). Recent WMAP measurements (see [31]) together with the LSS analysis has improved the limit: Σm ν f < 0.69 eV and hence, m ν f < 0.23 eV.…”

Neutrino mass limit from galaxy cluster number density evolution

“…When m ν > 10 −3 eV neutrinos are non-relativistic today [11] and thus behave like a hot component of dark matter. The presence of even a small fraction of massive neutrinos (hot dark matter) f ν ≡ Ω ν /Ω M , of order 10-20 %, requires a smaller value for the cosmological constant in comparison to a pure ΛCDM model, while other cosmological parameters are largely unaffected [6]. This is because a smaller Ω Λ results in a larger Ω M and hence a faster fluctuation growth rate, which compensates for the reduction of small-and intermediate-scale power caused by the neutrinos.…”

“…To compute P (k, z) we assume a close to scaleinvariant (Harrison-Peebles-Yu-Zeldovich) post-inflation energy density perturbation power spectrum P 0 (k) ∝ k n , with n ∼ 1, and we use a semi-analytical approximation for the transfer function T (k, z) in the ΛCDM model with three species of equal-mass neutrinos [41]. 6 For the 5 This is more consistent with estimates from WMAP data and from Big Bang nucleosynthesis using the mean of the primordial deuterium abundance measurements, but it is significantly larger than an estimate based on helium and lithium abundance measurements, see, e.g., Ref. [17].…”

“…[17]. 6 The effects of neutrino mass differences are irrelevant for our considerations, since if mν > 0.4 eV the mass eigenvalues are essentially degenerate [4], while if mν < 0.4 eV the mass differences do not much affect cluster number density evolution growth rate D(z) we use Eqs. (2)-(4) of Ref.…”

Neutrino mass matrix with approximate flavor symmetry

“…However, m 0 is constrained by WMAP data [10],3m 0 < 0.71 eV. When analyzed in conjunction with neutrino oscillation, it is found that mass eigenvalues are essentially degenerate with 3m 0 > 0.4 eV [11] The above limits put limits on ε : 7.9 × 10 −3 < ε < 2.5 × 10 −2 . It is pertinent to remark that in view of small mass differences involved [cf.…”