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Neutrino masses and the number of neutrino species from WMAP and 2dFGRS

Steen Hannestad

TL;DR

The paper analyzes cosmological constraints on neutrino properties using WMAP and 2dFGRS data, focusing on the sum of neutrino masses $\sum m_\nu$ and the effective relativistic energy density $N_\nu$. Through a full likelihood analysis within a flat $\Lambda$CDM framework and with careful treatment of bias and priors, the authors find $\sum m_\nu \lesssim 1.01$ eV (95% conf) when including SNIa and HST priors, while $N_\nu$ shows broad allowed ranges that tighten considerably when BBN information is included, yielding $N_\nu = 2.6^{+0.4}_{-0.3}$ (95% conf). They also explore how lepton asymmetry and late entropy production can affect $N_\nu$, and show that higher $N_\nu$ can relax the bound on $\sum m_\nu$, leaving room for LSND-like sterile neutrinos in some scenarios. Overall, the work highlights the strong dependence of neutrino constraints on priors and the potential tension between cosmology and certain terrestrial claims, while keeping open several nonstandard possibilities with early-universe physics.

Abstract

We have performed a thorough analysis of the constraints which can be put on neutrino parameters from cosmological observations, most notably those from the WMAP satellite and the 2dF galaxy survey. For this data we find an upper limit on the sum of active neutrino mass eigenstates of \sum m_nu < 1.0 eV (95% conf.), but this limit is dependent on priors. We find that the WMAP and 2dF data alone cannot rule out the evidence from neutrinoless double beta decay reported by the Heidelberg-Moscow experiment. In terms of the relativistic energy density in neutrinos or other weakly interacting species we find, in units of the equivalent number of neutrino species, N_nu, that N_nu = 4.0+3.0-2.1 (95% conf.). When BBN constraints are added, the bound on N_νis 2.6+0.4-0.3 (95% conf.), suggesting that N_nu could possibly be lower than the standard model value of 3. This can for instance be the case in models with very low reheating temperature and incomplete neutrino thermalization. Conversely, if N_nu is fixed to 3 then the data from WMAP and 2dFGRS predicts that 0.2458 < Y_P < 0.2471, which is significantly higher than the observationally measured value. The limit on relativistic energy density changes when a small $ν_e$ chemical potential is present during BBN. In this case the upper bound on N_nu from WMAP, 2dFGRS and BBN is N_nu < 6.5. Finally, we find that a non-zero \sum m_nu can be compensated by an increase in N_nu. One result of this is that the LSND result is not yet ruled out by cosmological observations.

Neutrino masses and the number of neutrino species from WMAP and 2dFGRS

TL;DR

The paper analyzes cosmological constraints on neutrino properties using WMAP and 2dFGRS data, focusing on the sum of neutrino masses and the effective relativistic energy density . Through a full likelihood analysis within a flat CDM framework and with careful treatment of bias and priors, the authors find eV (95% conf) when including SNIa and HST priors, while shows broad allowed ranges that tighten considerably when BBN information is included, yielding (95% conf). They also explore how lepton asymmetry and late entropy production can affect , and show that higher can relax the bound on , leaving room for LSND-like sterile neutrinos in some scenarios. Overall, the work highlights the strong dependence of neutrino constraints on priors and the potential tension between cosmology and certain terrestrial claims, while keeping open several nonstandard possibilities with early-universe physics.

Abstract

We have performed a thorough analysis of the constraints which can be put on neutrino parameters from cosmological observations, most notably those from the WMAP satellite and the 2dF galaxy survey. For this data we find an upper limit on the sum of active neutrino mass eigenstates of \sum m_nu < 1.0 eV (95% conf.), but this limit is dependent on priors. We find that the WMAP and 2dF data alone cannot rule out the evidence from neutrinoless double beta decay reported by the Heidelberg-Moscow experiment. In terms of the relativistic energy density in neutrinos or other weakly interacting species we find, in units of the equivalent number of neutrino species, N_nu, that N_nu = 4.0+3.0-2.1 (95% conf.). When BBN constraints are added, the bound on N_νis 2.6+0.4-0.3 (95% conf.), suggesting that N_nu could possibly be lower than the standard model value of 3. This can for instance be the case in models with very low reheating temperature and incomplete neutrino thermalization. Conversely, if N_nu is fixed to 3 then the data from WMAP and 2dFGRS predicts that 0.2458 < Y_P < 0.2471, which is significantly higher than the observationally measured value. The limit on relativistic energy density changes when a small chemical potential is present during BBN. In this case the upper bound on N_nu from WMAP, 2dFGRS and BBN is N_nu < 6.5. Finally, we find that a non-zero \sum m_nu can be compensated by an increase in N_nu. One result of this is that the LSND result is not yet ruled out by cosmological observations.

Paper Structure

This paper contains 12 sections, 7 equations, 6 figures.

Table of Contents

  1. introduction
  2. Absolute value of neutrino masses
  3. Likelihood analysis
  4. LSS data
  5. $k$-dependent bias
  6. CMB data
  7. Numerical results
  8. Neutrino masses
  9. Neutrino relativistic energy density
  10. Neutrino lepton asymmetry and $N_\nu$
  11. Combining $\sum m_\nu$ with $N_\nu$ - constraining LSND
  12. Discussion

Figures (6)

  • Figure 1: The top panel shows $\chi^2$ as a function of $\sum m_\nu$ for different choices of priors. The dotted line is for WMAP + 2dFGRS data alone, the dashed line is with the additional Wang et al. data. The full line is for additional HST and SNI-a priors as discussed in the text. The horizontal lines show $\Delta \chi^2 = 1$ and 4 respectively. The middle panel shows the best fit values of $H_0$ for a given $\sum m_\nu$. The horizontal lines show the HST key project $1\sigma$ limit of $H_0 = 72\pm 8 \,\, {\rm km}\,{\rm s}\,{\rm Mpc}^{-1}$. Finally, the lower panel shows best fit values of $\Omega_m$. In this case the horizontal line corresponds to the SNI-a $1\sigma$ upper limit of $\Omega_m < 0.42$.
  • Figure 2: $\chi^2$ as a function of $\sum N_\nu$ for different choices of priors. The dotted line is for WMAP data alone, the dashed line is with the additional Wang et al. and 2dFGRS data. The full line is for additional HST and SNI-a priors as discussed in the text.The horizontal lines show $\Delta \chi^2 = 1$ and 4 respectively. The middle panel shows the best fit values of $H_0$ for a given $N_\nu$. The horizontal lines show the HST key project $1\sigma$ limit of $H_0 = 72\pm 8 \,\, {\rm km}\,{\rm s}\,{\rm Mpc}^{-1}$. Finally, the lower panel shows best fit values of $\Omega_m$. In this case the horizontal line corresponds to the SNI-a $1\sigma$ upper limit of $\Omega_m < 0.42$.
  • Figure 3: 68% and 95% confidence contours in the $(\Omega_b h^2,N_\nu)$ plane for the WMAP TT and TE data, combined with the 2dFGRS data, the HST data on $H_0$ and the SNI-a data on $\Omega_m$.
  • Figure 4: 68% and 95% confidence contours in the $(\Omega_b h^2,N_\nu)$ plane for the same data sets as in fig. 3, but with the addition of BBN data. The lined contours are the 68% and 95% regions for BBN data alone.
  • Figure 5: The full lines show 68% and 95% confidence regions in the $(\Omega_b h^2,N_\nu)$ plane for the case where the additional $N_\nu$ is compensated during BBN by a small $\nu_e$ chemical potential. The full contours are for BBN data alone, whereas the dashed lines are for CMB and LSS data.
  • ...and 1 more figures