Probing physics beyond the standard model: limits from BBN and the CMB independently and combined

We present new Big Bang Nucleosynthesis (BBN) limits on the cosmic expansion rate or relativistic energy density, quantified via the number N_ν of equivalent neutrino species. We use the latest light element observations, neutron mean lifetime, and update our evaluation for the nuclear rates d + d ⟶ ³He + n and d + d ⟶ ³H+p. Combining this result with the independent constraints from the cosmic microwave background (CMB) yields tight limits on new physics that perturbs N_ν and η prior to cosmic nucleosynthesis: a joint BBN+CMB analysis gives N_ν = 2.898 ± 0.141, resulting in N_ν < 3.180 at 2σ. We apply these limits to a wide variety of new physics scenarios including right-handed neutrinos, dark radiation, and a stochastic gravitational wave background. The strength of the independent BBN and CMB constraints now opens a new window: we can search for limits on potential changes in N_ν and/or the baryon-to-photon ratio η between the two epochs. The present data place strong constraints on the allowed changes in N_ν between BBN and CMB decoupling; for example, we find -0.708 < N_ν^CMB - N_ν^BBN < 0.328 in the case where η and the primordial helium mass fraction Y_p are unchanged between the two epochs; we also give limits on the allowed variations in η or in (η, N_ν) jointly. We discuss scenarios in which such changes could occur, and show that BBN+CMB results combine to place important constraints on some early dark energy models to explain the H₀ tension. Looking to the future, we forecast the tightened precision for N_ν arising from both CMB Stage 4 measurements as well as improvements in astronomical ⁴He measurements. We find that CMB-S4 combined with present BBN and light element observation precision can give σ(N_ν) ≃ 0.03. Such future precision would reveal the expected effect of neutrino heating (N_eff-3 = 0.044) of the CMB during BBN, and would be near the level to reveal any particle species ever in thermal equilibrium with the standard model. Improved Y_p measurements can push this precision even further.