Observational constraints on secret neutrino interactions from big bang nucleosynthesis

We investigate possible interactions between neutrinos and massive scalar bosons via $g_{\varphi }\overline{\nu }\nu \varphi$ (or massive vector bosons via $g_V\overline{\nu }{\gamma }^{\mu }\nu V_{\mu }$) and explore the allowed parameter space of the coupling constant $g_{\varphi }$ (or $g_V$) and the scalar (or vector) boson mass $m_{\varphi }$ (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 $g_{\varphi }$ and $m_{\varphi }$ in the scalar-boson case is rather weak, due to a small number of degrees of freedom (d.o.f.). 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 $m_V\simeq 1\mathrm{MeV}$, while the bound becomes much weaker $g_V\lesssim 8\times {10}^{-6}$ for smaller masses $m_V\lesssim {10}^{-4}\mathrm{MeV}$. Moreover, we discuss in some detail how the SNIs affect the cosmological evolution and the abundances of the lightest elements.

Figure 1

The Feynman diagrams for the decay $\varphi \to \nu +\overline{\nu }$ (a), the annihilation $\nu +\overline{\nu }\to \varphi +\varphi$ (b1) and (b2), the elastic scattering $\nu +\varphi \to \nu +\varphi$ (c1) and (c2) processes in the presence of SNI with a massive scalar boson $\varphi$. The corresponding diagrams in the vector case can be obtained by replacing $\varphi$ with $V$ accordingly.

Figure 2

The contours of the extra radiation $\mathrm{\Delta }{N}_{\mathrm{eff}}\equiv N_{\mathrm{eff}}-3$ at $T_{\gamma }=1\mathrm{MeV}$ in the plane of $m_{\varphi }$ and $g_{\varphi }$ in the scalar-boson case (left panel) and in the plane of $m_V$ and $g_V$ in the vector-boson case (right panel). The shaded regions with dashed or dotted-dashed lines are excluded by weak decays of kaons and weak gauge bosons, which are reproduced from Ref. [51].

Figure 3

The cosmological evolution of the comoving energy densities for neutrinos $\nu$ (green curves), photons $\gamma$ (blue curves), and vector bosons $V$ (red curves) is presented in the left panel and that of the neutron-to-proton ratio $n/p$ (brown curves) and the helium mass fraction $Y_{\mathrm{p}}$ (purple curves) in the right panel. The plots (a1) and (a2) are given for $g_V={10}^{-4}$ and $m_V={10}^{-5}\mathrm{MeV}$ in Case I, while (b1) and (b2) for $g_V={10}^{-7}$ and $m_V=0.05\mathrm{MeV}$ in Case II. Note that the evolution of the comoving energy densities is plotted with respect to the scale factor $a(t)$ that has been normalized to $1/T_{\gamma }$ at very high temperatures. The dotted vertical lines at $a=1/\mathrm{MeV}$ or $T_{\gamma }=1\mathrm{MeV}$ in the plots (a1) and (b1) represent basically the epoch of neutrino decoupling. The dashed curves are for the standard theory, while the solid curves for the nonstandard one. The baryon-to-photon ratio $\eta$ takes on the value, which minimizes the ${\chi }^2$ function for each case.

Figure 4

The cosmological evolution of the comoving energy densities for neutrinos $\nu$ (green curves), photons $\gamma$ (blue curves), and vector bosons $V$ (red curves) is presented in the left panel and that of the neutron-to-proton ratio $n/p$ (brown curves) and the helium mass fraction $Y_{\mathrm{p}}$ (purple curves) in the right panel. The plots (a1) and (a2) are given for $g_V=2\times {10}^{-7}$ and $m_V=0.003\mathrm{MeV}$ in Case III, while (b1) and (b2) for $g_V={10}^{-6}$ and $m_V=2.5\mathrm{MeV}$ in Case IV. The notations and other input parameters are the same as for Fig. 3.

Figure 5

The evolutions of $g_{*}$ (left panel) and $N_{\mathrm{eff}}$ (right panel) with respect to $T_{\gamma }$ for different representative parameters: Case I: $g_V={10}^{-4}$ and $m_V={10}^{-5}\mathrm{MeV}$ (purple curve), Case II: $g_V={10}^{-7}$ and $m_V=0.05\mathrm{MeV}$ (green curve), Case III: $g_V=2\times {10}^{-7}$ and $m_V=0.003\mathrm{MeV}$ (blue curve), and Case IV: $g_V={10}^{-6}$ and $m_V=2.5\mathrm{MeV}$ (red curve). The dashed curve (horizontal dashed line) in the left (right) panel denotes the result in the standard case with instantaneous decoupling, while the vertical dotted line at $T_{\gamma }=1\mathrm{MeV}$ represents simply the epoch of neutrino decoupling.

Figure 6

The contour plot and density map of the ${\chi }^2$ function in the scalar-boson case (left panel) and those in the vector-boson case (right panel). Only the primordial mass fraction of helium $Y_{\mathrm{p}}=0.2449\pm 0.0040$ and the primordial abundance of deuterium $\mathrm{D}/\mathrm{H}{|}_{\mathrm{p}}=(2.53\pm 0.04)\times {10}^{-5}$ have been used in the statistical analysis.