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

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.

12 pages, 1 figure, updated to match PLB

References in corpus (3)

• A gravitational-wave probe of effective quantum gravity
• Resurrection of large lepton number asymmetries from neutrino flavor oscillations
• On the ambiguities in the effective action in Lorentz-violating gravity

Cited by in corpus (6)

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• Improved constraints on lepton asymmetry from the cosmic microwave background
• Probing neutrino interactions and dark radiation with gravitational waves
• Chiral gravitational effect in time-dependent backgrounds
• Chiral gravitational waves from thermalized neutrinos in the early Universe
• Gravitational Leptogenesis in Bounce Cosmology