Chiral gravitational waves from thermalized neutrinos in the early Universe

Abstract

We investigate polarized gravitational waves generated by chiral fermions in the early Universe. In particular, we focus on the contribution from left-handed neutrinos in thermal equilibrium with finite temperature and chemical potential in the radiation dominated era. We compute the correlation functions of gravitational fields pertinent to the Stokes parameter V characterizing the circular polarization of gravitational waves in the Minkowski and expanding spacetime backgrounds. In the expanding universe, we find that the thermalized neutrinos induce a non-vanishing V linear to the neutrino degeneracy parameter and wavenumber of gravitational waves in the long wavelength region. Possible future observations of such chiral gravitational waves could provide the information of the neutrino degeneracy parameter in the early Universe. C Derivation of eqs. (4.24)-(4.26) 29 C.1 Γ ± terms 29 C.2 Γ 0 term 30 C.2.1 Leading-order contribution 30 C.2.2 Next-to-leading-order contribution 31 D Derivation of eqs. (4.27) and (4.31) 31 D.1 Γ ± terms 31 D.2 Γ 0 term 32

Chiral effects in astrophysics and cosmology

“…Such a contribution may result in a different behavior of the gravitational waves, but a covariant description is desired to describe it in a consistent way. There are also other mechanisms for the generation of chiral GWs due to the presence of chiral fermions during inflation [291,292] and thermalized chiral fermions (like neutrinos) in the radiation dominated era [293].…”