Present bounds on the relativistic energy density in the Universe from cosmological observables

TL;DR

The paper investigates bounds on the relativistic energy density of the Universe, parameterized by $N_\nu^{\rm eff}$, using a broad set of cosmological probes spanning from BBN to the present: CMB temperature and polarization, LSS, BAO, Ly-α, SN-Ia, and primordial abundances. It employs a seven-parameter cosmological model fitted with Markov Chain Monte Carlo (cosmomc), linking $N_\nu^{\rm eff}$ to BBN predictions for $D/H$ and $Y_p$ via a dedicated code. The main results show $N_\nu^{\rm eff}=5.2^{+2.7}_{-2.2}$ (CMB+LSS) and $N_\nu^{\rm eff}=4.6^{+1.6}_{-1.5}$ (with Ly-α and BAO) at 95% c.l., indicating a mild tension with the standard value $N_\nu^{\rm eff}=3.046$, while BBN constraints prefer $N_\nu^{\rm eff}\sim 3.0$–$3.3$ depending on the helium abundance input. The work highlights that the data collectively favor $N_\nu^{\rm eff}$ in the 3–4 range, with improved $^3$He measurements potentially clarifying any epoch-dependent evolution of relativistic degrees of freedom. Future high-precision CMB data (e.g., PLANCK) and better primordial abundance measurements will sharpen these bounds and test for additional light relics or sterile species.

Abstract

We discuss the present bounds on the relativistic energy density in the Universe parameterized in terms of the effective number of neutrinos N using the most recent cosmological data on Cosmic Microwave Background (CMB) temperature anisotropies and polarization, Large Scale galaxy clustering from the Sloan Digital Sky Survey (SDSS) and 2dF, luminosity distances of type Ia Supernovae, Lyman-alpha absorption clouds (Ly-alpha), the Baryonic Acoustic Oscillations (BAO) detected in the Luminous Red Galaxies of the SDSS and finally, Big Bang Nucleosynthesis (BBN) predictions for 4He and Deuterium abundances. We find N= 5.2+2.7-2.2 from CMB and Large Scale Structure data, while adding Ly-alpha and BAO we obtain N= 4.6+1.6-1.5 at 95 % c.l.. These results show some tension with the standard value N=3.046 as well as with the BBN range N= 3.1+1.4-1.2 at 95 % c.l., though the discrepancy is slightly below the 2-sigma level. In general, considering a smaller set of data weakens the constraints on N. We emphasize the impact of an improved upper limit (or measurement) of the primordial value of 3He abundance in clarifying the issue of whether the value of N at early (BBN) and more recent epochs coincide.

Figures (3)

• Figure 1: Analysis from the first (more conservative) set of cosmological data (Left Panel) and including Lyman-$\alpha$ and BAO data (Right Panel). We show the marginalized contours at $68 \%$ and $95 \%$ c.l. on the $\omega_b$-$N_{\nu}^{\rm \it eff}$ plane along with the analogous contours from BBN using D and $^4$He (cnservative) experimental results reported in Eqs. (\ref{['deut']}) and (\ref{['4he']}) (dotted lines).
• Figure 2: The $^4$He mass fraction (Top left Panel) and D/H ratio (Bottom left Panel) from the first (more conservative) set of cosmological data versus $N_{\nu}^{\rm \it eff}$ (see text). We show the marginalized constraints at $68 \%$ and $95 \%$ c.l., while the regions between the two dashed horizontal lines are the 1-$\sigma$ experimental measurement bands. Plots on the right show the same results but adding BAO and Lyman-$\alpha$ data
• Figure 3: The $^7$Li/H (Top Left Panel) and $^3$He/H (Bottom Left Panel) from the first (more conservative) set of cosmological data versus $N_{\nu}^{\rm \it eff}$. We show the marginalized constraints at $68 \%$ and $95 \%$ c.l.. We also show the 1-$\sigma$ experimental upper limit on $^3$He/H of Eq. (\ref{['bound3he']}). The experimental results on $^7$Li/H are out of the chosen range. Plots on the right show the same results but adding BAO and Lyman-$\alpha$ data