The Case for Dark Radiation

TL;DR

The study investigates the presence of Dark Radiation by constraining the effective number of relativistic degrees of freedom, $N_{ m eff}$, and perturbation parameters $c_{ m eff}^2$ and $c_{ m vis}^2$ using a combined cosmological data set. It employs COSMOMC to analyze CMB data from WMAP7, ACT, SPT, and ACBAR and large-scale structure data, exploring two parametrizations: (i) a total $N_{ m eff}$ with full perturbations, and (ii) a standard 3-neutrino background plus an extra component with $N_{ m u}^S=N_{ m eff}-3.046$ and perturbations for the extra component only. The results show a preference for additional dark radiation with $N_{ m eff} o 4.08^{+0.71}_{-0.68}$ (fixed perturbations) or $N_{ m eff} o 3.89^{+0.70}_{-0.70}$ (free perturbations), and perturbation parameters $c_{ m eff}^2 o 0.312^{+0.026}_{-0.026}$ and $c_{ m vis}^2\to 0.29^{+0.21}_{-0.16}$, consistent with a relativistic free-streaming component. In the scenario with only the excess component varying, $N_{ u}^S$ is constrained to about $1.1$--$1.46$, with $c_{ m eff}^2\approx 0.24^{+0.08}_{-0.13}$ and little constraint on $c_{ m vis}^2$, indicating detectable extra radiation but potential nonstandard perturbations. A profile-likelihood analysis hints at a best-fit $N_{ m eff}\approx 3.88$, though the result is noisy, and Planck-era data are expected to tighten constraints to $\Delta N_{ m eff}\sim 0.2$.

Abstract

Combined analyses of recent cosmological data are showing interesting hints for the presence of an extra relativistic component, coined Dark Radiation. Here we perform a new search for Dark Radiation, parametrizing it with an effective number of relativistic degrees of freedom parameter, $\neff$. We show that the cosmological data we considered are clearly suggesting the presence for an extra relativistic component with $\neff=4.08_{-0.68}^{+0.71}$ at 95% c.l.. Performing an analysis on Dark Radiation sound speed $c_{\rm eff}$ and viscosity $c_{\rm vis}$ parameters, we found $\ceff=0.312\pm0.026$ and $\cvis=0.29_{-0.16}^{+0.21}$ at 95% c.l., consistent with the expectations of a relativistic free streaming component ($\ceff=\cvis$=1/3). Assuming the presence of 3 relativistic neutrinos we constrain the extra relativistic component with $\nnus=1.10_{-0.72}^{+0.79}$ and $\ceff=0.24_{-0.13}^{+0.08}$ at 95% c.l. while $\cvis$ results as unconstrained. Assuming a massive neutrino component we obtain further indications for Dark Radiation with $\nnus=1.12_{-0.74}^{+0.86}$ at 95% c.l. .

Figures (4)

• Figure 1: $68\%$ and $95\%$ c.l. constraints for the degeneracy between $N_{\rm {eff}}$ and the Hubble constant $H_0$, the age of the universe $t_0$, and the amplitude of mass fluctuations $\sigma_8$.
• Figure 2: $68\%$ and $95\%$ c.l. constraints for the degeneracy between neutrinos parameters. Red contours refer to model (A) in Table \ref{['delta_n']}, while blue contours show model (B).
• Figure 3: Degeneracy in the plane $\sum m_{\nu}-N_{\rm {\nu}}^S$ at 68% and 95% c.l. .
• Figure 4: Maximum Likelihood ratio $L_{N_{\rm {eff}}}/ L_{max}$ for $N_{\rm {eff}}$. The dashed lines represent the $68 \%$ and $95 \%$ c.l. for a Gaussian likelihood ($L_{N_{\rm {eff}}}/ L_{max}=0.6065$ and $L_{N_{\rm {eff}}}/ L_{max}=0.135$) respectively.