Observational Constraints on Secret Neutrino Interactions from Big Bang Nucleosynthesis

Abstract

We investigate possible interactions between neutrinos and massive scalar bosons via $g^{}_{\phi} \overline{\nu} \nu \phi$ (or massive vector bosons via $g^{}_V \overline{\nu} \gamma^\mu \nu V^{}_\mu$) and explore the allowed parameter space of the coupling constant $g^{}_{\phi}$ (or $g^{}_V$) and the scalar (or vector) boson mass $m^{}_\phi$ (or $m^{}_V$) by requiring that these secret neutrino interactions (SNIs) should not spoil the success of Big Bang nucleosynthesis (BBN). Incorporating the SNIs into the evolution of the early Universe in the BBN era, we numerically solve the Boltzmann equations and compare the predictions for the abundances of light elements with observations. It turns out that the constraint on $g^{}_{\phi}$ and $m^{}_\phi$ in the scalar-boson case is rather weak, due to a small number of degrees of freedom. However, in the vector-boson case, the most stringent bound on the coupling $g^{}_V \lesssim 6\times 10^{-10}$ at $95~\%$ confidence level is obtained for $m^{}_V \simeq 1~{\rm MeV}$, while the bound becomes much weaker $g^{}_V \lesssim 8\times 10^{-6}$ for smaller masses $m^{}_V \lesssim 10^{-4}~{\rm MeV}$. Moreover, we discuss in some detail how the SNIs affect the cosmological evolution and the abundances of the lightest elements.