A 2% determination of $N_{\mathrm{eff}}$ 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, $N_{\mathrm{eff}}$, 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 $Planck$, the Atacama Cosmology Telescope, and the South Pole Telescope, and baryon acoustic oscillation (BAO) data from the Dark Energy Spectroscopic Instrument, yielding $N_{\mathrm{eff}}=2.990\pm 0.070$ (68% C.L.). This is the tightest constraint on $N_{\mathrm{eff}}$ to date, and is in excellent agreement with the standard model prediction of $N_{\mathrm{eff}}=3.044$. Furthermore, we constrain excess contributions to $N_{\mathrm{eff}}$ beyond the three neutrino species, finding $\hat{I}”N_{\mathrm{eff}}<0.107$ (95% C.L.). This bound nearly approaches the minimum contribution to $\hat{I}”N_{\mathrm{eff}}$ from a light spin-3/2 particle that decoupled at any time after inflation ended. Our baseline analysis does not include large-scale $Planck$ polarization information, enabling a fully consistent combination of state-of-the-art CMB and BAO measurements. As a byproduct, we show that current $N_{\mathrm{eff}}$ bounds are essentially insensitive to the inclusion or exclusion of optical depth constraints inferred from large-scale CMB polarization data, making $N_{\mathrm{eff}}$ 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.

5 pages, 2 figures, 3 appendices. Prepared for submission to PRD. v2: minor changes and typos corrected