Gravitational waves induced by spinor fields

TL;DR

This paper calculates how massive spinor fields during inflation can generate scale-invariant gravitational waves, revealing a correction proportional to the fourth power of the Hubble parameter over the Planck mass, with complex mass dependence.

Contribution

It provides a detailed calculation of the gravitational wave contribution from single massive spinor fields during inflation using retarded Green propagators, highlighting scale-invariance and mass effects.

Findings

Correction is scale-invariant and of order (H^4/M_P^4).

Dependence on spinor mass is nontrivial when m_ψ ≳ H.

Results apply to arbitrary spinor masses during inflation.

Abstract

In realistic model-building, spinor fields with various masses are present. During inflation, spinor field may induce gravitational waves as a second order effect. In this paper, we calculate the contribution of single massive spinor field to the power spectrum of primordial gravitational wave by using retarded Green propagator. We find that the correction is scale-invariant and of order $H^4/M_P^4$ for arbitrary spinor mass $m_{\psi}$. Additionally, we also observe that when $m_\psi \gtrsim H$, the dependence of correction on $m_\psi/H$ is nontrivial.