WMAP 5-year constraints on lepton asymmetry and radiation energy density: Implications for Planck

TL;DR

This work investigates the radiation energy budget of the universe by constraining the effective number of relativistic species $N_{eff}$ and a possible leptonic asymmetry parameter $\xi_\nu$ using WMAP-5 year CMB data combined with additional CMB/LSS measurements and self-consistent BBN priors on the helium abundance $Y_p$. The authors implement leptonic asymmetric cosmologies with three degenerate neutrinos, modify CAMB/Recfast accordingly, and sample a $6+3$ dimensional parameter space, including $\Delta N^{oth}_{eff}$, with CosmoMC. They show that $N_{eff}$ is tightly constrained and that its inference is largely driven by the redshift of matter-radiation equality $z_{eq}$, not by neutrino anisotropic stress, and they obtain bounds such as $N_{eff}=3.026^{+0.638}_{-0.690}$ (68% CL, with $\xi_\nu=0$) and $-0.216\le \xi_\nu\le 0.226$ (68% CL). The Planck-like forecast indicates substantial improvements: $\sigma(N_{eff})\sim0.3$, $\sigma(\xi_\nu)\sim0.089$, and $\sigma(Y_p)\sim0.0133$, with $m_\nu$ bounds approaching ${\sim}0.44$ eV (95% CL). This work thus clarifies the role of lepton asymmetry and extra relativistic degrees of freedom in cosmology and guides expectations for Planck.

Abstract

In this paper we set bounds on the radiation content of the Universe and neutrino properties by using the WMAP-5 year CMB measurements complemented with most of the existing CMB and LSS data (WMAP5+All),imposing also self-consistent BBN constraints on the primordial helium abundance. We consider lepton asymmetric cosmological models parametrized by the neutrino degeneracy parameter and the variation of the relativistic degrees of freedom, due to possible other physical processes occurred between BBN and structure formation epochs. We find that WMAP5+All data provides strong bounds on helium mass fraction and neutrino degeneracy parameter that rivals the similar bounds obtained from the conservative analysis of the present data on helium abundance. We also find a strong correlation between the matter energy density and the redshift of matter-radiation equality, z_re, showing that we observe non-zero equivalent number of relativistic neutrinos mainly via the change of the of z_re, rather than via neutrino anisotropic stress claimed by the WMAP team. We forecast that the CMB temperature and polarization measurements observed with high angular resolutions and sensitivities by the future Planck satellite will reduce the errors on these parameters down to values fully consistent with the BBN bounds.

Figures (4)

• Figure 1: The marginalized posterior likelihood probabilities of the main cosmological parameters obtained for: WMAP5+All with $\Delta N^{oth}_{eff}=0$ and $\xi_{\nu}=0$ priors (black lines), WMAP5+All with $\xi_{\nu}=0$ prior (green lines), WMAP5+All with no neutrino priors (blue lines) and Planck-like simulated data with no neutrino priors (red lines).
• Figure 2: The marginalized posterior likelihood probabilities of the neutrino mass, $m_{\nu}$, degeneracy parameter, $\xi_{\nu}$, leptonic asymmetry, $L_{\nu}$, helium mass fraction, $Y_p$, and redshift of matter-radiation equality, $z_{eq}$, for: WMAP5+All with $\Delta N^{oth}_{eff}=0$ and $\xi_{\nu}=0$ priors (black lines), WMAP5+All with $\xi_{\nu}=0$ prior (green lines), WMAP5+All with no neutrino priors (blue lines) and Planck-like simulated data with no neutrino priors (red lines).
• Figure 3: Two-dimensional marginalized joint probability distributions (68% and 95% CL) showing the degeneracy between: $\Omega_mh^2$ and $N_{eff}$ (left panel) and $\Omega_mh^2$ and $z_{eq}$ (right panel). The thick solid lines in the left panel show the 68% and 95% CL limits calculated from the corresponding limits on $z_{eq}$ obtained form the WMAP5+All with $\xi_{\nu}=0$ prior by using equation (10). The contours show: WMAP5+All with $\Delta N^{oth}_{eff}=0$ and $\xi_{\nu}=0$ priors (black lines), WMAP5+All with $\xi_{\nu}=0$ prior (green lines), WMAP5+All with no neutrino priors (blue lines) and Planck-like simulated data with no neutrino priors (red lines).
• Figure 4: Two-dimensional marginalized joint probability distributions (68% and 95% CL) showing the degeneracy between: $Y_p$ and $N_{eff}$ (left panel) and $N_{eff}$ and $\xi_{\nu}$ (right panel). The contours show: WMAP5+All with $\xi_{\nu}=0$ prior (green lines), WMAP5+All with no neutrino priors (blue lines) and Planck-like simulated data with no neutrino priors (red lines).