Baryogenesis in $f(R)$ theories of gravity

$f(R)$-theories of gravity are reviewed in the context of the so called gravitational baryogenesis. The latter is a mechanism for generating the baryon asymmetry in the Universe, and relies on the coupling between the Ricci scalar curvature $R$ and the baryon current. Gravity Lagrangians of the form $\mathcal{L}(R)\sim R^n$, where $n$ differs from 1 (the case of the General Relativity) only for tiny deviations of a few percent, are consistent with the current bounds on the observed baryon asymmetry.

Figure 1

Plot of the function $g_{\alpha }$ vs $\alpha$. The range in which the function $g_{\alpha }$ is positive, hence $T$ is defined, is $0.155\lesssim \alpha \le 1/2$.

Figure 2

$T_f$ vs $\alpha$. In this plot the parameter $\alpha$ assumes values $\gtrsim 0.15506$.

Figure 3

$T_f$ vs $\alpha$. In this plot the parameter $\alpha$ assumes values $\le 0.5$.

Figure 4

Plot of ${\Lambda }_{\alpha }$ vs $\alpha$. The dashed line represents the upper bound 1.6. The maximum value $\sim 1.59$, corresponding to $\alpha \simeq 0.4845$, agrees with the estimate (19). Moreover, in the limit $\alpha \to 1/2$, ${\Lambda }_{\alpha }$ vanishes, so no net baryon asymmetry is generated (in agreement with General Relativity).