Energy conditions and gravitational baryogenesis in $f(R, {\cal R})$ gravity

TL;DR

The paper investigates energy conditions in hybrid metric-Palatini gravity, focusing on the model $f(R,\mathcal{R})=R+\alpha\mathcal{R}^{n}$, and demonstrates that the strong energy condition can be violated for some $n$, enabling accelerated expansion. It then reformulates the theory in a scalar-tensor representation via auxiliary fields and a conformal transformation to the Einstein frame, deriving the corresponding effective energy density and pressure and their energy-condition inequalities. The authors compute the gravitational baryogenesis mechanism in this hybrid gravity, proposing a CP-violating interaction driven by curvature and deriving the baryon-to-entropy ratio; they show compatibility with the observed value in radiation- and matter-dominated epochs for plausible parameter ranges. Overall, the work shows that hybrid metric-Palatini gravity can accommodate cosmic acceleration and provide a curvature-based route to baryogenesis, offering a framework to test gravity–matter couplings beyond GR.

Abstract

In this work, first we examine the energy conditions in the context of the generalized metric-Palatini hybrid gravity, known as $f(R, {\cal R})$ gravity. We show that for the proposed model in this study, {\it i.e.} $ f(R, {\cal R})= R +α{\cal R}^{n} $, one of the four fundamental energy conditions, specifically the strong energy condition, does not hold for some values of $n$. Therefore, it seems that hybrid gravity can provide a model for the accelerated expansion of the universe. In continuation of completing our study in this work, we try to analyze the impact of hybrid metric-Palatini gravity on the gravitational baryogenesis process. The hybrid metric-Palatini model combines two gravitational theories that allow for a more detailed examination of the behavior of space-time and its interaction with matter. This combination is critical in the early radiation-dominant universe, where unusual gravitational effects may play a key role in generating baryonic asymmetry and the production of baryons and anti-baryons.

Figures (4)

• Figure 1: Behavior of the WEC for $\rho^{eff}\geqslant 0$ as a function of $n$, with $H_{0} = 67.6 ~km s^{-1} Mpc^{-1}$, $q_{0} = -0.81$, $j_{0} = 2.16$, $s_{_{0}} = -0.35$, $\alpha=2$, and $\kappa = 1$, where $3 < n < 30$ (left). Behavior of the WEC for $\rho^{eff}+p^{eff}\geqslant 0$ as a function of $n$ (right).
• Figure 2: Behavior of the SEC for $\rho^{eff}+3p^{eff}\geqslant 0$ as a function of $n$, with $H_{0} = 67.6 ~km s^{-1} Mpc^{-1}$, $q_{0} = -0.81$, $j_{0} = 2.16$, $s_{_{0}} = -0.35$, $\alpha=2$, and $\kappa = 1$, where $3 < n < 30$ (left). Behavior of the SEC for $\rho^{eff}+3p^{eff}\geqslant 0$ as a function of $n$, where $0.5 < n < 1.9$ (right).
• Figure 3: Behavior of the WEC for $\rho^{eff}\geqslant 0$ as a function of $n, m$, with $H_{0} = 67.6~ km s^{-1} Mpc^{-1}$, $\rho =p=0$, $W=1$, $\alpha=\beta=1$, and $\kappa = 1$, where $0 < n < 1000$ and $0 < m < 1000$ (left). Behavior of the WEC for $\rho^{eff}+p^{eff}\geqslant 0$ as a function of $n, m$ for $W=e^{-\frac{\sqrt{2\kappa}\alpha }{\sqrt{3}}}$ (right).
• Figure 4: Behavior of the $\frac{n_{b}}{s}$ as a function of $\alpha$, with$M_{*}=9\times 10^{18} GeV$, $T_D=10^{11}GeV$, $t = 10^{-13} s$, $0.115 <\alpha<2$, for $\omega = 0$ (left) and $\omega = \frac{1}{3}$ (right).