Lepton asymmetry leading to baryogenesis by primordial black holes

TL;DR

This paper proposes a novel mechanism where primordial black holes induce lepton asymmetry through neutrino energy splitting, leading to baryogenesis consistent with observations, by considering gravitational effects on neutrino properties.

Contribution

It introduces a new leptogenesis mechanism involving gravitational effects on neutrinos near primordial black holes, incorporating non-Hermitian terms in the Dirac Lagrangian in curved spacetime.

Findings

Primordial black holes of mass ~10^{12} g can produce the observed baryon asymmetry.

Lepton asymmetry of order 10^{-10} is generated via neutrino energy splitting.

The mechanism is effective until nucleosynthesis, linking black hole physics to baryogenesis.

Abstract

Baryogenesis remains an unresolved problem in cosmology, with existing mechanisms facing significant caveats. We show that the effects of primordial black holes (PBHs) on neutrinos produce the lepton asymmetry $\sim 10^{-10}$ which subsequently produces the baryon asymmetry. We consider the Dirac Lagrangian in curved spacetime in local coordinates exhibiting Hermitian pseudo-vector and non-Hermitian vector terms. These terms lead to energy splitting between weakly interacting neutrinos and antineutrinos, resulting in their unequal number densities and hence a lepton asymmetry. While the non-Hermitian effect leads to a non-conserved total probability of neutrinos, the leptogenesis due to gravitational effects of a PBH could be significant until the nucleosynthesis era. This in turn produces baryon asymmetry from the symmetry of lepton and baryon numbers via the sphaleron process in the electro-weak era. We show that in the most conservative scenario, the PBHs of mass $\sim 10^{12}$ g and spin $\sim 0.01$ produce the observed baryogenesis at temperature 130 GeV, when such PBHs are available abundantly. However, massive PBHs also could produce the observed asymmetry, assuming the non/anti-Hermitian vector couplings for neutrino and anti-neutrino get canceled from the Lagrangian, leading the system to be Hermitian.