Constraints on neutrino and dark radiation interactions using cosmological observations

TL;DR

This paper develops a two-parameter framework to characterize the perturbations of the cosmic dark radiation background via cosmological observations, introducing the rest-frame sound speed $c_{\rm eff}^2$ and the viscosity parameter $c_{\rm vis}^2$. Using a compilation of CMB and LSS data, including WMAP, ACT, SPT, SDSS, and Lyman-$\alpha$, the authors constrain these parameters alongside the effective number of relativistic species $N_{\rm eff}$, finding that the standard $(N_{\rm eff},c_{\rm eff}^2)=(3,1/3)$ is disfavored at high confidence when $c_{\rm vis}^2$ and $c_{\rm eff}^2$ are fixed, and remains disfavored at about 95–97% CL when these parameters are allowed to vary. The analysis shows marginal preferences for $N_{\rm eff}>3$ and $c_{\rm eff}^2$ near $0.31$, with $c_{\rm vis}^2$ around $1/3$, and discusses the impact of allowing the helium fraction $Y_p$ to vary. Forecasts indicate Planck-like data will dramatically improve constraints to $N_{\rm eff}=3.0\pm0.17$, $c_{\rm vis}^2=0.333\pm0.026$, and $c_{\rm eff}^2=0.333\pm0.004$, enabling tighter tests of new radiative degrees of freedom.

Abstract

Observations of the cosmic microwave background (CMB) and large-scale structure (LSS) provide a unique opportunity to explore the fundamental properties of the constituents that compose the cosmic dark radiation background (CDRB), of which the three standard neutrinos are thought to be the dominant component. We report on the first constraint to the CDRB rest-frame sound speed, ceff^2, using the most recent CMB and LSS data. Additionally, we report improved constraints to the CDRB viscosity parameter, cvis^2. For a non-interacting species, these parameters both equal 1/3. Using current data we find that a standard CDRB, composed entirely of three non-interacting neutrino species, is ruled out at the 99% confidence level (C.L.) with ceff^2 = 0.30 +0.027 -0.026 and cvis^2 = 0.44 +0.27 -0.21 (95% C.L.). We also discuss how constraints to these parameters from current and future observations (such as the Planck satellite) allow us to explore the fundamental properties of any anomalous radiative energy density beyond the standard three neutrinos.

Figures (3)

• Figure 1: The evolution of the neutrino density perturbation in its rest-frame for a mode with $k=0.1\ h {\rm Mpc}^{-1}$ where $h$ is the Hubble parameter in units of 100 km/(s Mpc), as a function of the scale-factor, $a$, or the conformal time, $\tau$. The black solid curve gives the evolution for the standard case, i.e., when ${c^{2}_{\rm vis}} ={c^{2}_{\rm eff}}= 1/3$. The left-hand panel shows the evolution when ${c^{2}_{\rm vis}} = 0$ (red, dot-dashed) and ${c^{2}_{\rm vis}} = 1$ (blue, dashed) with ${c^{2}_{\rm eff}} =1/3$. With ${c^{2}_{\rm vis}} = 0$ (red, dot-dashed) the CDRB becomes a perfect fluid leading to undamped acoustic oscillations. The right-hand panel shows the evolution when ${c^{2}_{\rm eff}} = 0.1$ (red, dot-dashed) and ${c^{2}_{\rm eff}} = 0.8$ (blue, dashed) with ${c^{2}_{\rm vis}} =1/3$. When ${c^{2}_{\rm eff}}$ is small (red, dot-dashed) the CDRB is partially able to overcome its internal pressure support and nearly cluster. The bottom panels show the corresponding evolution of the Newtonian potential, $\Phi_N$.
• Figure 2: Modifications to the CMB temperature power-spectrum, $C_l^{TT}$, as both ${c^{2}_{\rm vis}}$ (top panel) and ${c^{2}_{\rm eff}}$ (bottom panel) are varied in the same way as in Fig. \ref{['fig:evo']}: the black solid curve gives the evolution for the standard case; the top panel shows $C_l^{TT}$ when ${c^{2}_{\rm vis}} = 0$ (red, dot-dashed) and ${c^{2}_{\rm vis}} = 1$ (blue, dashed); the bottom panel shows ${c^{2}_{\rm eff}} = 0.2$ (red, dot-dashed) and ${c^{2}_{\rm eff}} =0.7$ (blue, dashed). The large angular scale measurements are from the 7-year WMAP release WMAP7 and on small angular scales from ACT ACT.
• Figure 3: Two dimensional contours (68% and 95% C.L.) showing the degeneracy between ${c_{\rm vis}}$/$n_s$ and ${c_{\rm eff}}$/${N_{\rm eff}}$. The dotted contours show the constraints when only CMB data is used. The blue-dashed contours show the constraints when restricting the CMB to just WMAP7 and large-scale structure data, excluding the Lyman-alpha data. The thin-solid contours show constraints when restricting the CMB to just WMAP7 and with all large-scale structure data. The thick contours show the constraints when all of the data are included. The blue circle shows that the standard value of ${c^{2}_{\rm eff}}= 1/3$ and ${N_{\rm eff}} = 3$ is excluded at slightly higher than the 95% C.L.