A 2% determination of $N_{\rm eff}$ from primordial element abundance, cosmic microwave background, and baryon acoustic oscillation measurements

Abstract

We present a new constraint on the effective number of relativistic species in the early universe, $N_{\rm eff}$, by combining recent primordial helium abundance measurements from the Large Binocular Telescope $Y_p$ Project with primordial deuterium abundance data, cosmic microwave background (CMB) observations from $\it{Planck}$, the Atacama Cosmology Telescope, and the South Pole Telescope, and baryon acoustic oscillation (BAO) data from the Dark Energy Spectroscopic Instrument, yielding $N_{\rm eff}=2.990\pm0.070$ (68% C.L.). This is the tightest constraint on $N_{\rm eff}$ to date, and is in excellent agreement with the standard model prediction of $N_{\rm eff}=3.044$. Furthermore, we constrain excess contributions to $N_{\rm eff}$ beyond the three neutrino species, finding $ΔN_{\rm eff}<0.107$ (95% C.L.). This bound nearly approaches the minimum contribution to $ΔN_{\rm eff}$ from a light spin-3/2 particle that decoupled at any time after inflation ended. Our baseline analysis does not include large-scale $\it{Planck}$ polarization information, enabling a fully consistent combination of state-of-the-art CMB and BAO measurements. As a byproduct, we show that current $N_{\rm eff}$ bounds are essentially insensitive to the inclusion or exclusion of optical depth constraints inferred from large-scale CMB polarization data, making $N_{\rm eff}$ highly robust in this regard. Our constraints place stringent limits on light particles in the early Universe and on a broad range of models aimed at increasing the CMB-inferred value of the Hubble constant.

Figures (9)

• Figure 1: Comparison of $N_{\rm eff}$ constraints from dataset combinations considered here. For each dataset, we show the one-dimensional marginalized posterior mean and the 68% two-tailed confidence limits. The gray constraint uses only primordial helium and deuterium abundance measurements. For the remaining datasets, the $\times$ and the square denote constraints excluding and including primordial helium and deuterium abundance measurements, respectively. The measurements with solid (dashed) error bars exclude (include) Planck low-$\ell$ EE measurements. The vertical dot-dashed line shows the Standard Model prediction, $N_{\rm eff}=3.044.$
• Figure 2: Constraints on additional relativistic degrees of freedom in the early Universe. The light (dark) gray shaded region denotes $\Delta N_{\rm eff} > 0.107$ ($0.0913$), which is excluded at the 95% C.L. using primordial abundance, CMB, and BAO data (primordial abundance and CMB data). In both cases, do not include low-$\ell$ EE data. The solid curves show theoretical predictions for $\Delta N_{\rm eff}$ as a function of the particle decoupling temperature for bosons and fermions with different numbers of internal degrees of freedom, $g$. The vertical blue bands denote the approximate regions of neutrino decoupling and the QCD phase transition. This figure is based on Refs. Aghanim:2018eyxSimonsObservatory:2018kocACT:2025tim.
• Figure 3: Two-dimensional marginalized posterior for the six $\Lambda$CDM parameters, as well as $N_{\rm eff}$ and $Y_P^{\rm BBN}$, for the main datasets considered here. Note that these results do not include low-$\ell$ EE data. This figure does not impose any external priors on primordial elemental abundances (see Fig. \ref{['fig:full_posterior_with_abundance_info']}).
• Figure 4: Same as Fig. \ref{['fig:full_posterior_no_abundance_info']}, except including measurements of the primordial helium and deuterium abundance.
• Figure 5: Comparison of constraints on $H_0r_d$, $\Omega_m$, and $N_{\rm eff}$ inferred from our CMB-PAS dataset and DESI. We show the CMB-PAS results with and without Planck low-$\ell$ EE measurements. Without low-$\ell$ EE data, the CMB and BAO measurements are statististically consistent and, hence, can be safely combined.