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.

arXiv comment25 pages, 5 tables and 4 figures. This version is accepted for publication in European Physical Journal C

References in corpus (53)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• The Cosmological Constant and Dark Energy
• Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies
• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R) theories
• Cosmological Imprint of an Energy Component with General Equation of State
• A Phantom Menace? Cosmological consequences of a dark energy component with super-negative equation of state
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Quintessence, Cosmic Coincidence, and the Cosmological Constant
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• A Dynamical Solution to the Problem of a Small Cosmological Constant and Late-time Cosmic Acceleration
• k-Inflation
• Essentials of k-essence
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results
• Exponential potentials and cosmological scaling solutions
• Kinetically Driven Quintessence
• Curvature Quintessence
• Quintessence and the Rest of the World
• Everything You Always Wanted To Know About The Cosmological Constant Problem (But Were Afraid To Ask)
• Cosmology with a Primordial Scaling Field
• Ghost Condensation and a Consistent Infrared Modification of Gravity
• Conditions for the cosmological viability of f(R) dark energy models
• Curvature quintessence matched with observational data
• Structure formation with a self-tuning scalar field
• Are f(R) dark energy models cosmologically viable ?
• Dynamical systems applied to cosmology: dark energy and modified gravity
• The Cosmology of f(R) Gravity in the Metric Variational Approach
• Phantom crossing, equation-of-state singularities, and local gravity constraints in f(R) models
• Phase-Space analysis of Teleparallel Dark Energy
• Energy Conditions and Stability in $f(R)$ theories of gravity with non-minimal coupling to matter
• Dynamical behavior in $f(T,T_G)$ cosmology
• Haloes of k-Essence
• Phase-space analysis of Horava-Lifshitz cosmology
• Autonomous Dynamical System Approach for $f(R)$ Gravity
• Dynamical Systems Perspective of Cosmological Finite-time Singularities in $f(R)$ Gravity and Interacting Multifluid Cosmology
• Power-laws f(R) theories are cosmologically unacceptable
• Dynamical analysis of generalized Galileon cosmology
• Dynamical system analysis of generalized energy-momentum-squared gravity
• Phantom dark energy with varying-mass dark matter particles: acceleration and cosmic coincidence problem
• Dark energy: investigation and modeling
• Dynamical system analysis at background and perturbation levels: Quintessence in severe disadvantage comparing to $\Lambda$CDM
• Dynamical stability of K-essence field interacting non-minimally with a perfect fluid
• Full Investigation on the Dynamics of Power-Law Kinetic Quintessence
• Dynamical Stability in presence of non-minimal derivative dependent coupling of $k$-essence field with a relativistic fluid
• 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
• Realising Interactions Between Dark Matter and Dark Energy Using $k$-essence Cosmology
• Implications of JLA data for $k-$essence model of dark energy with given equation of state
• Time-dependent diffusive interactions between dark matter and dark energy in the context of $k-$essence cosmology
• Diffusive dark matter and dark energy scenario and $k-$essence in the context of Supernova Ia observations

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• Spherically Symmetric Potentials in Quadratic $f(R)$ Gravity
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• Observational and Thermodynamic aspects of one-dimensional Dark Energy EoS parametrization models