Collective neutrino-antineutrino pair oscillations

In dense neutrino gas, pairing correlations between neutrinos and antineutrinos with opposite momenta can be nonzero in generalized neutrino quantum kinetic equations at the mean-field level. In this Letter, we investigate for the first time the condition under which collective neutrino-antineutrino ($\nu\bar\nu$) pairing instabilities can occur, using simplified toy models consisting of discretized $\nu\bar\nu$ pairs in a homogeneous neutrino gas. We find that, in ansiotropic systems, $\nu\bar\nu$ pairing instabilities generally emerge when the phase space distribution of the excessive pair-occupation number, defined as the sum of the neutrino and antineutrino occupation numbers of a pair minus 1, changes signs. The associated instability growth rate is set by the forward scattering potential and is comparable to that of collective fast neutrino flavor instabilities. The instabilities can result in pair conversions of $\nu\bar\nu$ occupation numbers between different momentum modes. Our results motivate further studies to assess the relevance of $\nu\bar\nu$ pairing effects in realistic astrophysical and cosmological environments.