Signals from Fermionic inflationary cosmology with Yukawa interaction

TL;DR

The paper analyzes an inflationary scenario in which the inflaton couples directly to a Dirac fermion via a Yukawa term $g\phi\bar{\psi}\psi$, deriving exact analytic solutions for the Dirac field in quasi-de Sitter space. The authors obtain Hankel/Bessel mode functions parameterized by the dimensionless mass $\tilde{m}=(m+g\phi)/H$ and slow-roll corrections, and quantify fermion production through adiabatic and non-adiabatic components, including the backreaction on inflation. They compute the scalar and tensor perturbations sourced by the fermionic field and show that the tensor-to-scalar ratio $r$ is suppressed when $\tilde{m}\gtrsim1$ by approximately $1/(1+2.95\pi^2 g^2)$, while for $\tilde{m}\ll1$ the predictions reduce to standard single-field inflation. The framework provides high-energy-scale inflation with consistent observational bounds and yields detailed predictions for fermion density, equation of state, and sourced perturbations, highlighting a controllable non-adiabaticity via the Yukawa coupling $g$.

Abstract

We investigate an inflationary model wherein the Dirac field $ψ$ is directly coupled to a scalar inflaton $φ$ via a Yukawa interaction $gφ\barψψ$ 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 $\langle n\rangle$ indicates that the Yukawa interaction strength $g$ is to characterize the degree of non-adiabaticity. For large value of the dimensionless effective mass $\tilde m=(m+gφ)/H$, i.e. $\tilde m\gtrsim 1$, the tensor-to-scalar ratio $r$ is suppressed by a factor of approximately $1/(1+2.95π^2g^2)$. 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.

Figures (4)

• Figure 1: Slow-roll parameter $\varepsilon$ versus $\tilde{m}$ for different values of the interaction strength g.
• Figure 2: Equation of state parameter $\omega$ versus $\tilde{m}$ for different values of the interaction strength g.
• Figure 3: Comoving fermionic pair density $\langle n\rangle/H^3$ as a function of the dimensionless effective mass $\tilde{m}$ with $g$=0.01, 0.1, 1, and 10, respectively.
• Figure 4: Tensor-to-scalar ratio $r/16\varepsilon_0$ as a function of dimensionless effective mass $\tilde{m}$ for different values of Yukawa coupling constant $g$, where $\varepsilon_0=1.25\times10^{-3}$.