Probing Physics Beyond the Standard Model: Limits from BBN and the CMB Independently and Combined

Abstract

We present new Big Bang Nucleosynthesis (BBN) limits on the cosmic expansion rate or relativistic energy density, quantified via the number $N_{\nu }$ of equivalent neutrino species. We use the latest light element observations, neutron mean lifetime, and update our evaluation for the nuclear rates $d+d\to He3+n$ and $d+d\to H3+p$. Combining this result with the independent constraints from the cosmic microwave background (CMB) yields tight limits on new physics that perturbs $N_{\nu }$ and $\eta$ prior to cosmic nucleosynthesis: a joint BBN+CMB analysis gives $N_{\nu }=2.898\pm 0.141$, resulting in $N_{\nu }<3.180$ at $2\sigma$. We apply these limits to a wide variety of new physics scenarios including right-handed neutrinos, dark radiation, and a stochastic gravitational wave background. We also search for limits on potential {\em changes} in $N_{\nu }$ and/or the baryon-to-photon ratio $\eta$ between the two epochs. The present data place strong constraints on the allowed changes in $N_{\nu }$ between BBN and CMB decoupling; for example, we find $-0.708<N_{\nu }^{\mathrm{CMB}}-N_{\nu }^{\mathrm{BBN}}<0.328$ in the case where $\eta$ and the primordial helium mass fraction $Y_p$ are unchanged between the two epochs; we also give limits on the allowed variations in $\eta$ or in $(\eta ,N_{\nu })$ jointly. Looking to the future, we forecast the tightened precision for $N_{\nu }$ arising from both CMB Stage 4 measurements as well as improvements in astronomical \he4 measurements. We find that CMB-S4 combined with present BBN and light element observation precision can give $\sigma (N_{\nu })\simeq 0.03$. Such future precision would reveal the expected effect of neutrino heating ($N_{\mathrm{eff}}-3=0.044$) of the CMB during BBN, and would be near the level to reveal any particle species ever in thermal equilibrium with the standard model.

40 pages, 12 figures

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