We investigate the impact of a nonminimal coupling between curvature and inflaton field within the 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 nonminimally 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. Afterward, 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 nonminimal coupling term de facto increases inflaton mass for negative values of $\xi$, letting fermion-antifermion decays be more probable and thus enhancing the overall baryogenesis process. Quite the opposite, the baryon asymmetry is reduced for positive values of the coupling 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.

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• Baryogenesis & leptogenesis
• Inflation
• Large scale structure of the Universe
• Relativistic aspects of cosmology