Gravitational baryogenesis in $F(R)$ gravity's rainbow

We investigate the gravitational baryogenesis scenario within the context of $F(R)$ gravity’s rainbow which incorporates both modified gravity and energy-dependent spacetime. This study explores a mechanism for generating baryon asymmetry based on the interaction between the derivative of the Ricci scalar $R$ and the baryon current within the framework of $F(R)$ gravity’s rainbow. The rainbow functions, arising from quantum gravity effects, modify the gravitational interaction and the Friedmann equations, leading to a distinct evolution of the baryon asymmetry compared to standard $F(R)$ gravity. We analyze the conditions under which a viable baryon asymmetry can be produced, taking into account the constraints from cosmological observations and the specific form of the $F(R)$ function. By examining the cosmological equations in the context of $F(R)$ gravity’s rainbow, we obtain power-law solutions for these equations. We also identify the decoupling temperature and the ratio of baryonic number to entropy density in this model, depending on the model’s parameters. First, we discuss the acceptable intervals of the model’s parameters which are defined by constraints on the background quantity. We note that the decoupling temperature and the ratio of baryon-to-entropy in these models depend on the value of the rainbow function. We compare the predictions of this model with the existing observational data. Our results suggest that $F(R)$ gravity’s rainbow provides a novel mechanism for gravitational baryogenesis, potentially explaining the observed baryon asymmetry in the universe while incorporating quantum gravity corrections.

💡 Research Summary

This paper presents a detailed investigation of the gravitational baryogenesis mechanism within the framework of F(R) gravity coupled with the “Gravity’s Rainbow” formalism. The primary goal is to explain the observed matter-antimatter asymmetry of the universe (the Baryon Asymmetry of the Universe, BAU) by leveraging the interplay between modified gravity and quantum gravity effects.

The core mechanism under study is gravitational baryogenesis, where a coupling between the derivative of the Ricci scalar (∂μR) and the baryon current (Jμ) violates CPT symmetry dynamically in an expanding universe, thereby generating a net baryon number. The paper embeds this mechanism into a novel theoretical framework that combines two key extensions of General Relativity (GR): 1) F(R) gravity, where the Einstein-Hilbert action is generalized to an arbitrary function F(R) of the Ricci scalar, and 2) Gravity’s Rainbow, which introduces an energy-dependent spacetime metric via “rainbow functions” ˜f(E) and ˜g(E), capturing putative quantum gravity effects near the Planck scale.

The analysis begins by deriving the modified field equations for F(R) gravity within the rainbow metric background. The authors adopt a power-law parameterization for the rainbow function (˜f ≈ (H/M)^α, with α>0) and assume a power-law expansion of the universe (scale factor a(t) ∝ t^γ, with γ>1). They then solve these equations analytically for two simplified cases: Case I where ˜f = ˜g, and Case II where ˜g = 1. For each case, explicit expressions for the Ricci scalar R, the energy density ρ, and other cosmological quantities are derived as functions of cosmic time and the model parameters (α, γ, n, B), where F(R) is assumed to be of the form F(R) = B R^n.

The gravitational baryogenesis process is then analyzed within this setup. Using the effective interaction term (∂μR Jμ)/M_*^2, the paper derives the decoupling temperature T_D (the temperature at which the baryon-number-violating interactions fall out of thermal equilibrium) and, crucially, the final baryon-to-entropy ratio Y_B = n_B/s. The resulting expression for Y_B is presented as a function of the model’s parameters, explicitly showing its dependence on the rainbow parameter α. This highlights how quantum gravity corrections, encoded in the rainbow functions, can directly influence the efficiency of baryogenesis.

Finally, the paper conducts a numerical analysis to test the model’s viability. By plugging in various values for the parameters α and n, the authors compute the predicted Y_B and compare it with the stringent observational constraint from Cosmic Microwave Background measurements: Y_B ≈ 0.87 × 10^{-10}. The results demonstrate that for certain regions of the parameter space (particularly with n slightly greater than 1), the model can successfully reproduce the observed baryon asymmetry. The analysis confirms that the rainbow parameter α plays a significant role in modulating the magnitude of Y_B.

In conclusion, the study argues that F(R) gravity’s rainbow provides a novel and theoretically motivated framework for gravitational baryogenesis. It successfully integrates modifications from both extended gravity theories and quantum gravity considerations, offering a potential explanation for the BAU that is consistent with cosmological observations. This work bridges high-energy physics, early universe cosmology, and quantum gravity phenomenology.