Gravitational Instabilities of the Cosmic Neutrino Background with Non-zero Lepton Number

TL;DR

This paper explores how a non-zero lepton number in the cosmic neutrino background causes gravitational instabilities, leading to birefringent gravitational waves and vacuum decay, with implications for early universe conditions.

Contribution

It explicitly computes the quantum-generated gravitational Chern-Simons term in a lepton asymmetric neutrino background, revealing novel gravitational effects.

Findings

Gravitational waves exhibit birefringence depending on lepton asymmetry.

Negative energy graviton modes induce rapid vacuum decay.

Constraints on lepton asymmetry from radiation energy density.

Abstract

We argue that a cosmic neutrino background that carries non-zero lepton charge develops gravitational instabilities. Fundamentally, these instabilities are related to the mixed gravity-lepton number anomaly. We have explicitly computed the gravitational Chern-Simons term which is generated quantum-mechanically in the effective action in the presence of a lepton number asymmetric neutrino background. The induced Chern-Simons term has a twofold effect: (i) gravitational waves propagating in such a neutrino background exhibit birefringent behaviour leading to an enhancement/suppression of the gravitational wave amplitudes depending on the polarisation, where the magnitude of this effect is related to the size of the lepton asymmetry; (ii) Negative energy graviton modes are induced in the high frequency regime, which leads to very fast vacuum decay producing, e.g., positive energy photons and negative energy gravitons. From the constraint on the present radiation energy density, we obtain an interesting bound on the lepton asymmetry of the universe.