Baryogenesis in Nonminimally Coupled $f(R)$ Theories

TL;DR

This paper explores how nonminimal $f(R)$ gravity theories can generate the observed baryon asymmetry through a curvature-current coupling, showing small deviations from General Relativity are sufficient and compatible with early universe conditions.

Contribution

It extends gravitational baryogenesis mechanisms to nonminimally coupled $f(R)$ models, identifying parameter ranges consistent with observations and primordial nucleosynthesis.

Findings

Small deviations from GR can produce the observed baryon asymmetry.

Power-law coupling functions with $0 < n \,\lesssim\, 0.078$ are viable.

The characteristic curvature scale for these models is established.

Abstract

We generalize the mechanism for gravitational baryogensis in the context of $f(R)$ theories of gravity, including a nonminimal coupling between curvature and matter. In these models, the baryon asymmetry is generated through an effective coupling between the Ricci scalar curvature and the net baryon current that dynamically breaks Charge Conjugation, Parity and Time Reversal (CPT) invariance. We study the combinations of characteristic mass scales and exponents for both non-trivial functions present in the modified action functional and establish the allowed region for these parameters: we find that very small deviations from General Relativity are consistent with the observed baryon asymmetry and lead to temperatures compatible with the subsequent formation of the primordial abundances of light elements. In particular, we show the viability of a power-law nonminimal coupling function $f_2(R) \sim R^n$ with $ 0 < n \lesssim 0.078 $ and determine its characteristic curvature scale.