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 $\Delta N_{\rm eff}<0.107$ (95% C.L.). This bound nearly approaches the minimum contribution to $\Delta N_{\rm eff}$ 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.