Signals from Fermionic inflationary cosmology with Yukawa interaction

Abstract

We investigate an inflationary model wherein the Dirac field $\psi$ is directly coupled to a scalar inflaton $\varphi$ via a Yukawa interaction $g\varphi \overline{\psi }\psi$ and examine the resulting observational implications. Within the slow-roll approximation, we derive analytical solutions of the Dirac equations during inflation. The analytical result on the fermion pair density $〈n〉$ indicates that the Yukawa interaction strength $g$ is to characterize the degree of non-adiabaticity. For large value of the dimensionless effective mass $\tilde{m}=(m+g\varphi )/H$, i.e. $\tilde{m}\gtrsim 1$, the tensor-to-scalar ratio $r$ is suppressed by a factor of approximately $1/(1+2.95{\pi }^2{g}^2)$. This condition is also characterized by a significant backreaction. Conversely, if $\tilde{m}\ll 1$, the value of $r$ remains consistent with that observed in standard cold inflation. Our analysis is performed under the assumption of the highest inflationary energy scales compatible with current observational constraints.