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 gravitylepton 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 of a vacuum state into, 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.

Improved constraints on lepton asymmetry from the cosmic microwave background

“…On the other hand, η l is still allowed to exceed η b by many orders of magnitude, which could have interesting consequences for physics at T > T BBN [17,18,38].…”

Chiral gravitational effect in time-dependent backgrounds

“…We here give a brief review of the formulation in ref. [69] (see also ref. [82]), which is consistent with ref.…”

“…Note that a similar discussion has been studied in ref. [69] where the authors consider the effect of an asymmetric fermion background, namely the cosmic neutrino background, to the propagating gravitational wave during the matter-dominated era, through the gravitational Chern-Simons term in the effective Lagrangian. Nevertheless, we should note that there are non-local thermal and chemical potential corrections found in refs.…”

“…Such a dynamics has been taken into account in ref. [69] where the effect of the cosmic neutrino background on the propagating gravitational waves through the induced gravitational Chern-Simons term is considered. We here give a brief review of the formulation in ref.…”

“…(2.1)) modifies the propagator of the fermion, which in turn gives the parity-violating contribution to the graviton polarization tensor Π µνρσ through the loop correction as depicted in figure 1. In the massless limit of the fermion m k, the leading parity-violating correction to the polarization tensor from the fermion loop takes the following simple form in the momentum space [69]:…”