Dynamical analysis of coupled curvature-matter scenario in viable $f(R)$ dark energy models at de Sitter phase

Abstract

We explore the interaction between dark matter and curvature-driven dark energy within viable $f(R)$ gravity models, employing the phase-space analysis approach of linear stability theory. By incorporating an interacting term, denoted as $\mathcal{Q}=\alpha H{\tilde{\rho }}_{\mathrm{m}}\left(\frac{{\kappa }^2}{3H^2}{\rho }_{\mathrm{curv}}+1\right)$, into the continuity equations of both sectors, we examine dynamics of two $f(R)$ gravity models that adhere to local gravity constraints and fulfill cosmological viability criteria. In de Sitter phase, our investigation reveals modifications of critical points compared to the conventional form, attributed to the introduced interaction. Through a comprehensive phase-space analysis, we illustrate the trajectories near critical points and outline the constraints on the phase space based on cosmological and cosmographic parameters. Furthermore, we can also observe stable behavior of this interacting system during the de Sitter phase of the universe.

18 pages, 2 tables and 6 figures. This version is accepted for publication in Classical and Quantum Gravity

References in corpus (13)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results
• Conditions for the cosmological viability of f(R) dark energy models
• Are f(R) dark energy models cosmologically viable ?
• The Cosmology of f(R) Gravity in the Metric Variational Approach
• Power-laws f(R) theories are cosmologically unacceptable
• Dynamical stability of K-essence field interacting non-minimally with a perfect fluid
• Full Investigation on the Dynamics of Power-Law Kinetic Quintessence
• Investigating the accelerated expansion of the Universe through updated constraints on viable $f(R)$ models within the metric formalism
• Dynamical Stability in presence of non-minimal derivative dependent coupling of $k$-essence field with a relativistic fluid
• Dynamical stability in models where dark matter and dark energy are non-minimally coupled to curvature
• Cosmological dynamics of interacting dark energy and dark matter in viable models of f(R) gravity
• Ghost condensates and pure kinetic $k$-essence condensates in presence of field-fluid non-minimal coupling in the dark sector

Cited by in corpus (4)

• 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
• Observational and Thermodynamic aspects of one-dimensional Dark Energy EoS parametrization models