Cosmological dynamics of f(R) models in dynamical system analysis

Abstract

In this work we try to understand the late time acceleration of the universe by assuming some modification in the geometry of the space and using dynamical system analysis. This technique allows to understand the behavior of the universe without analytically solving the field equations. We study the acceleration phase of the universe and stability properties of the critical points which could be compared with observational results. We consider an asymptotic behavior of two particular models $f(R)=R-\mu R_c\frac{(R/R_c{)}^{2n}}{(R/R_c{)}^{2n}+1}$ and $f(R)=R-\mu R_c\left[1-(1+R^2/R_c^2{)}^{-n}\right]$ with $n,\mu ,R_c>0$ for the study. As a first case we fix the value of $\mu$ and analyzed for all $n$. Later as second case, we fix the value of $n$ and calculation are done for all $\mu$. At the end all the calculations for the generalized case have been shown and results have been discussed in detail.

arXiv comment17 pages

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
• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R) theories
• Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
• f(R,T) gravity
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Disappearing cosmological constant in f(R) gravity
• Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe
• Thermodynamical Aspects of Gravity: New insights
• Conditions for the cosmological viability of f(R) dark energy models
• Are f(R) dark energy models cosmologically viable ?
• The Large Scale Structure of f(R) Gravity
• Finite-time future singularities in modified Gauss-Bonnet and $\mathcal{F}(R,G)$ gravity and singularity avoidance
• Equation of state for dark energy in $f(T)$ gravity
• f(R) Gravity and scalar-tensor theory
• Extended Gravity Cosmography
• Reconstruction of $f(T)$ gravity: Rip cosmology, finite-time future singularities and thermodynamics
• Causes of Irregular Energy Density in $f(R,T)$ Gravity
• Scalar-Tensor Models of Normal and Phantom Dark Energy
• The role of energy conditions in $f(R)$ cosmology
• Thermodynamics of cosmological horizons in $f(T)$ gravity
• Inflationary universe from perfect fluid and $F(R)$ gravity and its comparison with observational data
• A bird's eye view of f(R)-gravity
• Traversable Wormholes and Energy Conditions with Two Different Shape Functions in $f(R)$ Gravity
• Autonomous Dynamical System Approach for $f(R)$ Gravity
• Notes on wormhole existence in scalar-tensor and F(R) gravity
• Dynamical Systems Perspective of Cosmological Finite-time Singularities in $f(R)$ Gravity and Interacting Multifluid Cosmology
• Trace-anomaly driven inflation in $f(T)$ gravity and in minimal massive bigravity
• Role of Tilted Congruence and $f(R)$ Gravity on Regular Compact Objects
• No realistic wormholes from ghost-free scalar-tensor phantom dark energy
• $f(R)$ constant-roll inflation
• Generalized Second Law of Thermodynamics in $f(T)$ Gravity with Entropy Corrections
• Effective $F(T)$ gravity from the higher-dimensional Kaluza-Klein and Randall-Sundrum theories
• Dynamical systems approach and generic properties of $f(T)$ cosmology
• Cosmology Based on f(R) Gravity Admits 1 eV Sterile Neutrinos
• Phantom boundary crossing and anomalous growth index of fluctuations in viable f(R) models of cosmic acceleration
• Phase Space Analysis of the Accelerating Multi-fluid Universe
• Viable Inflationary Models in a Ghost-free Gauss-Bonnet Theory of Gravity
• Stability analysis for cosmological models in $f(R)$ gravity using dynamical system analysis
• Dynamical analysis on $f(R,\mathcal{G})$ cosmology
• Cosmological constraints and comparison of viable $f(R)$ models
• Reconstruction of Slow-roll $F(R)$ Gravity Inflation from the Observational Indices
• Future Oscillations around Phantom Divide in f(R) Gravity
• f(R) Gravity and its Cosmological Implications
• Dynamical system analysis of interacting models
• Dynamical system analysis of dark energy models in scalar coupled metric-torsion theories
• Once again on thin-shell wormholes in scalar-tensor gravity
• Phase Space description of Nonlocal Teleparallel Gravity
• Qualitative behavior of cosmological models combining various matter fields

Cited by in corpus (3)

• FRW Cosmology in $f(Q,T)$ Gravity
• Stability analysis of f(Q) gravity models using dynamical systems
• Generic autonomous system approach to interacting dark energy models