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

E Grohs,George M Fuller

doi:10.1016/j.nuclphysb.2016.08.034

Abstract

The weak interaction charged current processes (νe+n↔p+e−; ν¯e+p↔n+e+; n↔p+e−+ν¯e) interconvert neutrons and protons in the early universe and have significant influence on Big Bang Nucleosynthesis (BBN) light-element abundance yields, particularly that for 4He. We demonstrate that the influence of these processes is still significant even when they operate well below temperatures T∼0.7 MeV usually invoked for “weak freeze-out,” and in fact down nearly into the alpha-particle formation epoch (T≈0.1 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 keV.

Highlights

In this paper we examine individual charged current weak interactions in the Big Bang Nucleosynthesis (BBN) epoch and uncover a feature of these which is surprising and explains how BBN can be sensitive to any physics which
Weak Freeze-Out” (WFO), and aspects of nuclear statistical equilibrium (NSE) freeze-out, all occur more or less contemporaneously over many, many Hubble times. This fact dictates the use of a numerical approach to BBN, first done by Refs. [12, 13], but it sets up the sensitivity to late-changing weak interactions and their dependence on neutrino distribution functions which we examine in this paper
Other weak interactions on nuclei are present during BBN [14], but we focus on the n ↔ p rates for this work

Summary

Introduction

In this paper we examine individual charged current weak interactions in the Big Bang Nucleosynthesis (BBN) epoch and uncover a feature of these which is surprising and explains how BBN can be sensitive to any physics which. The rates of neutron-to-proton converting (i.e., isospin-changing) weak interactions decrease as the temperature drops and, eventually the n/p ratio will be dominated by neutron decay The former decoupling process is termed “weak decoupling”, while the latter is dubbed “Weak Freeze-Out” (WFO). For Tcm > Teq, the creation term (dYn/dt)+ is larger than the Hubble rate, and vice versa for Tcm < Teq. In our calculations, we assume neutrinos instantaneously decoupled from the plasma at a comoving temperature parameter Tcm > Teq. The nucleosynthesis effects from the altered WFO scenarios dwarf the contributions from neutrino energy transport In order to account for the contribution of each rate to either the neutron or proton abundance change, we will write the Boltzmann equations as the following.

Results

First scenario

Second scenario

Third scenario

Fourth scenario

Conclusion