Probing the Effective Number of Neutrino Species with Cosmic Microwave Background

TL;DR

The paper addresses constraining the effective number of neutrino species $N_\nu$ using cosmic microwave background data alone, testing compatibility with the standard value $N_\nu = 3.046$ and exploring possible extra radiation. The authors first discuss how $N_\nu$ affects the CMB power spectrum, notably via the radiation density, the timing of radiation-matter equality, the acoustic scale, and neutrino free-streaming, and provide derivative relations to illustrate parameter degeneracies. They then perform a Markov chain Monte Carlo analysis using WMAP5, ACBAR, BOOMERANG, and CBI, exploring scenarios with $Y_p$ free, fixed, or linked to a BBN relation, and forecast Planck's potential constraints. They find $0.96 \le N_\nu \le 7.94$ (95% CL) with $Y_p$ free, $1.39 \le N_\nu \le 6.38$ under the BBN relation, and a Planck-era forecast of $2.68 \le N_\nu \le 3.44$ (95% CL) with the BBN relation, demonstrating that CMB data—without LSS—can probe relativistic energy content and test early-universe physics, especially when high-$l$ data and BBN priors are included.

Abstract

We discuss how much we can probe the effective number of neutrino species N_nu with cosmic microwave background alone. Using the data of WMAP, ACBAR, CBI and BOOMERANG experiments, we obtain a constraint on the effective number of neutrino species as 0.96< N_nu <7.94 at 95% C.L. for a power-law LCDM flat universe model. The limit is improved to be 1.39 < N_nu < 6.38 at 95% C.L. if we assume that the baryon density, N_nu and the helium abundance are related by the big bang nucleosynthesis theory. We also provide a forecast for the PLANCK experiment using a Markov chain Monte Carlo approach. In addition to constraining N_nu, we investigate how the big bang nucleosynthesis relation affects the estimation for these parameters and other cosmological parameters.

Figures (4)

• Figure 1: CMB power spectra for the cases with $N_\nu=1$ (blue dotted line), $3$ (red solid line) and $5$ (green dashed line). Other cosmological parameters are taken as the mean value from WMAP5 alone analysis for a power-law flat $\Lambda$CDM model.
• Figure 2: 1D posterior distributions of $N_\nu$. The red solid line uses WMAP5 alone (with $Y_p=0.24$ fixed) and the other lines use WMAP5+ACBAR+BOOMERANG+CBI with different assumptions on $Y_p$. The green dashed line fixes it to be $Y_p=0.24$, the blue dotted line uses the BBN relation to fix $Y_p$ from $\omega_b$ and $N_\nu$, and the magenta dot-dashed line treats $Y_p$ as a free parameter. For the analysis with WMAP5 alone, we assumed the prior on the cosmic age as $10~{\rm Gyr} < t_0 < 20~{\rm Gyr}$.
• Figure 3: The 68% and 95% allowed regions in the plane of $N_\nu$ v.s. other parameters when WMAP5 alone is used with $Y_p=0.24$ (red solid line), WMAP5+ACBAR+BOOMERANG+CBI are used with $Y_p=0.24$ (green dashed line), $Y_p$ being fixed by the BBN relation (blue dotted line) and $Y_p$ being treated as a free parameter (orange and yellow shaded region).
• Figure 4: An illustration of the degeneracy of $N_\nu$ with other cosmological parameters. Here the value of the effective number of neutrino are assumed as $N_\nu=1$ (blue dotted line), $3$ (red solid line) and $5$ (green dashed line) and other cosmological parameters are chosen such that CMB spectra becomes the same as that with the fiducial parameters.