Modulational instabilities in neutrino-antineutrino interactions

Using a semiclassical approach, we analyze the collective behavior of neutrinos and antineutrinos in a dense background. Applying the Wigner transform technique, we show that the interaction can be modeled by a coupled system of nonlinear Vlasov-like equations. From these equations, we derive a dispersion relation for neutrino-antineutrino interactions on a general background. The dispersion relation admits a novel modulational instability. Moreover, we investigate the modifications of the instability due to thermal effects. The results are examined, together with a numerical example, and we discuss the induced density inhomogeneities using parameters relevant to the early Universe.