Gravitational waves induced by spinor fields

In realistic model building, spinor fields with various masses are present. During inflation, a spinor field may induce gravitational waves as a second order effect. In this paper, we calculate the contribution of a single massive spinor field to the power spectrum of primordial gravitational wave by using a 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.

Figure 1

The $r$-dependence of Eq. (17). We see that when $r\gtrsim 1$, the Dirac field may contribute negatively or positively to the power spectrum of gravitational wave, depending on the value of $r$, i.e., $m_{\psi }/H$. For clearer demonstration we plot result for various ranges of $r$ in different panels.