Baryogenesis in nonminimally coupled $f(R)$ theories

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 nontrivial 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.

Figure 1

Allowed regions for the exponents $(n,m)$: ${\alpha }^{-}$ and ${\alpha }^{+}$ correspond to $0<\alpha <1/2$ and $\alpha >1/2$, respectively. From lighter to darker shade, $T_D=\{1,2,3\}\times {10}^{16}\mathrm{GeV}$.

Figure 2

Baryon-to-entropy ratio ${\eta }_S$ contour plot for the choice $M_1=M_2=M_P$ and $T_D=3.3\times {10}^{16}\mathrm{GeV}$.

Figure 3

Same as Fig. 2, but with $T_D=2\times {10}^{16}\mathrm{GeV}$.

Figure 4

Dependence of $M_1$ on the exponent $m$ for different choices of the decoupling temperature $T_D$.

Figure 5

Dependence of $M_2$ on the exponent $n$ for different choices of the decoupling temperature $T_D$.