The surprising influence of late charged current weak interactions on Big Bang Nucleosynthesis

Abstract

The weak interaction charged current processes (${\nu }_e+n\leftrightarrow p+e^{-}$, ${\bar{\nu }}_e+p\leftrightarrow n+e^{+}$, $n\leftrightarrow p+e^{-}+{\bar{\nu }}_e$) interconvert neutrons and protons in the early universe and have significant influence on Big Bang Nucleosynthesis (BBN) light-element abundance yields, particulary that for ${}^4\mathrm{He}$. We demonstrate that the influence of these processes is still significant even when they operate well below temperatures $T\sim 0.7\mathrm{MeV}$ usually invoked for "weak freeze-out," and in fact down nearly into the alpha-particle formation epoch ($T\approx 0.1\mathrm{MeV}$). This physics is correctly captured in commonly used BBN codes, though this late-time, low-temperature persistent effect of the isospin-changing weak processes, and the sensitivity of the associated rates to lepton energy distribution functions and blocking factors are not widely appreciated. We quantify this late-time influence by analyzing weak interaction rate dependence on the neutron lifetime, lepton energy distribution functions, entropy, the proton-neutron mass difference, and Hubble expansion rate. The effects we point out here render BBN a keen probe of any beyond-standard-model physics that alters lepton number/energy distributions, even subtly, in epochs of the early universe all the way down to near $T=100\mathrm{keV}$.

Comments: 27 pages, 8 figures