Dynamics of viable $f(R)$ dark energy models in the presence of Curvature-Matter interactions

Abstract

In this study, we analyze the dynamics of the interaction between dark matter and curvature-driven dark energy in viable $f(R)$ gravity models using the framework of dynamical system analysis. We incorporate this interaction by introducing a source term in their respective continuity equations, given by $Q=\frac{{\kappa }^2\alpha }{3H}{\tilde{\rho }}_{\mathrm{m}}{\rho }_{\mathrm{curv}}$, and examine two $f(R)$ gravity models that comply with local gravity constraints and cosmological viability criteria. Our findings reveal subtle modifications to fixed points and their stability criteria when compared to the conventional dynamical analysis of $f(R)$ gravity models without matter-curvature interactions as proposed and examined in prior literature. We determine the parameter limits associated with the stability criteria of critical points of the dynamical system for both the models. Additionally, the introduction of interaction reveals variations in the dynamical aspects of cosmic evolution, contingent on the range of values for the relevant model parameters. These results are consistent with the observed features of cosmic evolution within specific limits of the $f(R)$ models parameters and the coupling parameter $\alpha$. We also examine the evolutionary dynamics of the universe in the interacting scenario through cosmological and cosmographic parameters. Our analysis demonstrates that the interacting scenario comprehensively accounts for all the observed phases of the universe's evolution and also results in a stable late-time cosmic acceleration. Additionally, we've studied how the coupling parameter affects evolutionary dynamics, particularly its impact on the matter-to-curvature energy density ratio. Our findings suggest that the chosen form of interaction can also address the cosmic coincidence problem.

25 pages, 5 tables and 4 figures. This version is accepted for publication in European Physical Journal C

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• Chaotic interactions between dark matter and dark energy
• Constructing Viable Interacting Dark Matter and Dark Energy Models: A Dynamical Systems Approach
• Exploring the evolution of structure growth in the universe with field-fluid interactions through dynamical stability analysis
• Observational constraints on generic models of non-minimal curvature-matter coupling
• A comprehensive dynamical and phenomenological analysis of structure growth in curvature-modulated coupled quintessence scenario
• Spherically Symmetric Potentials in Quadratic $f(R)$ Gravity
• Linearized Gravity in the Starobinsky Model: Perturbative Deviations from General Relativity
• Observational and Thermodynamic aspects of one-dimensional Dark Energy EoS parametrization models