Constraints on the cosmic neutrino background

TL;DR

The paper constrains the relativistic energy density of the early Universe, expressed as the effective number of neutrino species $N_{eff}$, using CMB and LSS data while allowing for non-zero spatial curvature. A COSMOMC-based Bayesian analysis of WMAP, CBI, and 2dF is performed, revealing that flat-Universe analyses bias $N_{eff}$ downward and that curvature shifts the constraints toward higher values; with broad priors, $N_{eff}$ can be as large as $\sim7$ at 95% CL, and best-fit values lie near $N_{eff}\approx4$. Including an $H_0$ prior tightens the bounds (e.g., $1.9 \le N_{eff} \le 6.62$ with best-fit $N_{eff}=4.08$), while supernovae data do not significantly improve the constraints. The work highlights degeneracies with $\Omega_k$ and $\Omega_{dm}h^2$ and argues that independent measurements of $\sigma_8$ and $H_0$, along with small-scale power data, are needed to break these degeneracies and better characterize the cosmic neutrino background.

Abstract

The radiative component of the Universe has a characteristic impact on both large scale structure (LSS) and the cosmic microwave background radiation (CMB). We use the recent WMAP data, together with previous CBI data and 2dF matter power spectrum, to constrain the effective number of neutrino species $N_{eff}$ in a general Cosmology. We find that $N_{eff}=4.31$ with a 95 per cent C.L. $1.6 \le N_{eff} \le 7.1$. If we include the $H_0$ prior from the HST project we find the best fit $N_{eff}=4.08$ and $1.90 \le N_{eff} \le 6.62$ for 95 per cent C.L. The curvature we derive is still consistent with flat, but assuming a flat Universe from the beginning implies a bias toward lower $N_{eff}$, as well as artificially smaller error bars. Adding the Supernovae constraint doesn't improve the result. We analyze and discuss the degeneracies with other parameters, and point out that probes of the matter power spectrum on smaller scales, accurate independent $σ_8$ measurements, together with better independent measurement of $H_0$ would help in breaking the degeneracies.

Figures (2)

• Figure 1: The marginalized likelihoods for the parameters under consideration. We have assumed here a top--hat prior on $H_0$ corresponding to the 1$\sigma$ interval allowed by the HST key project results. The solid line is for a general curvature, the dotted corresponds to the flat Universe case. The general curvature tends to push the constraints on $N_{eff}$ toward higher values. The same upper limits on $N_{eff}$ are probably due to the upper limit imposed on $H_0$ ($<80$). Notice that $z_{re}$ in the range considered here is not constrained by the data.
• Figure 2: The marginalized likelihoods in the case of a general cosmology. The short--dashed line only consider CMB+2dF data, the dotted includes the $H_0$ prior from the HST project, and the solid also includes SN data. $N_{eff}$ is restricted to be $\le 6.6$ at 95 per cent C.L., and $\Omega_k$ tends to be negative but is still consistent with flat. Note the high $n_s$ and $z_{re}$ values. The long--dashed line is obtained adding an hypothetical prior on $\sigma_8$ with the typical scaling from clusters and weak lensing.