Consequences of non-minimal coupling for mass mixing in spontaneous baryogenesis

TL;DR

This paper studies how a non-minimal coupling between curvature and inflaton affects baryogenesis, showing it enhances particle production and inflaton decay, thereby increasing baryon asymmetry in the early universe.

Contribution

It introduces a detailed analysis of non-minimal Yukawa-like coupling effects on inflaton decay and baryogenesis, including mass-mixing and cosmic expansion considerations.

Findings

Non-minimal coupling enhances inflaton decay into fermions.

The coupling increases the effective inflaton mass, boosting baryon production.

Mass-mixing effects influence the fermionic fields and baryon asymmetry.

Abstract

We investigate the impact of a non-minimal Yukawa-like coupling between curvature and inflaton field within the \emph{spontaneous baryogenesis} background. We demonstrate that this coupling leads to a significant enhancement in particle production, even for small values of the coupling constant $\xi$. Assuming a perfectly homogeneous and isotropic universe during the reheating phase, we study the inflaton decay into fermion-antifermion pairs by means of a semiclassical approach, treating fermions as quantized fields and considering the inflaton and the Ricci scalar as classical quantities. We adopt the simplest approach in which the inflaton is minimally coupled to baryons, and non-minimally with gravity. In particular, we solve the equations of motion for the inflaton to first order in perturbation theory, with $\xi$ serving as perturbative parameter. Afterwards, we compute the difference in the number densities of baryons and antibaryons produced through the inflaton decay into fermion-antifermion pairs. We show that the non-minimal coupling term \emph{de facto} increases inflaton mass, letting fermion-antifermion decays be more probable, and thus enhancing the overall baryogenesis process. As a further outcome, we find that the non-minimal Yukawa coupling also leads to a renormalization of the inflaton mass and weakly influences the bounds over the gravitational constant. Finally, since the fermionic fields appear not to be mass eigenstates, we specialize the mass-mixing between them only. To this end, we thus include the effects of mass-mixing and cosmic expansion into our calculations. Physical consequences of baryon production are therefore explored.