Limits on Dark Radiation, Early Dark Energy, and Relativistic Degrees of Freedom

TL;DR

This paper investigates whether excess relativistic energy in the early Universe arises from sterile neutrinos, early dark energy (EDE), or barotropic dark energy. It models these components and analyzes current data with COSMOMC/CAMB, along with Planck-era forecasts, to constrain the EDE density $\Omega_e$, the effective number of relativistic species $N_{\rm eff}$, and the primordial helium abundance $Y_p$, while identifying observational signatures such as the ISW effect. The results show no strong evidence for standard EDE and place tight bounds on $\Omega_e$ and $\Delta N_{\rm eff}^{EDE}$, but demonstrate that barotropic DE can mimic a neutrino background and substantially alter inferred $N_{\rm eff}$ and $Y_p$, challenging a straightforward interpretation of extra radiation. Planck-quality data will be able to distinguish among sterile neutrinos, EDE, and barotropic DE, reducing degeneracies and informing early-Universe physics and inflationary dynamics, including potential shifts in the inflationary tilt $n_s$.

Abstract

Recent cosmological data analyses hint at the presence of an extra relativistic energy component in the early universe. This component is often parametrized as an excess of the effective neutrino number N_{eff} over the standard value of 3.046. The excess relativistic energy could be an indication for an extra (sterile) neutrino, but early dark energy and barotropic dark energy also contribute to the relativistic degrees of freedom. We examine the capabilities of current and future data to constrain and discriminate between these explanations, and to detect the early dark energy density associated with them. We found that while early dark energy does not alter the current constraints on N_{eff}, a dark radiation component, such as that provided by barotropic dark energy models, can substantially change current constraints on N_{eff}, bringing its value back to agreement with the theoretical prediction. Both dark energy models also have implications for the primordial mass fraction of Helium Y_p and the scalar perturbation index n_s. The ongoing Planck satellite mission will be able to further discriminate between sterile neutrinos and early dark energy.

Figures (5)

• Figure 1: Evolution of $\Delta N_{\rm {eff}}^{EDE}$ as a function of the scale factor $a$, for $\Omega_{\rm e}=0.05$ (the results scale nearly linearly for smaller values). Note the strong time dependence near recombination.
• Figure 2: CMB temperature (top panel) and ISW contribution alone (bottom panel) angular power spectra dependence from sterile neutrinos, early dark energy and barotropic dark energy. All the models have been chosen to produce one extra relativistic degree of freedom at the epoch of BBN, except for the solid curve showing the standard case.
• Figure 3: 68% and 95% c.l. contours in the $Y_p$-$\Omega_{\rm e}$ plane for the standard EDE model. The red dashed contours show the $c_{\rm s}^{2}=c_{\rm vis}^2=1/3$ model, while the blue solid contours show the $c_{\rm s}^{2}=1, c_{\rm vis}^2=0$ model. Since the early dark energy enhances the expansion rate during the BBN, it allows for a higher primordial Helium mass fraction according to $\Delta Y_p \simeq 0.013 (N_{\rm {eff}}-3)$steigman.
• Figure 4: 68% and 95% c.l. contours in the $N_{\rm {eff}}^{\nu}$-$\Omega_{\rm e}$ plane for the standard EDE model plus neutrinos). The red dashed contours refer to $c_{\rm s}^{2}=c_{\rm vis}^2=1/3$ case, while the blue solid contours refer to the $c_{\rm s}^{2}=1, c_{\rm vis}^2=0$ case.
• Figure 5: 68% and 95% c.l. contours in the $N_{\rm {eff}}^{\nu}$-$\Omega_{\rm e}^B$ plane for the barotropic dark energy model.