Cosmological dynamics of R^n gravity

Abstract

A detailed analysis of dynamics of cosmological models based on $R^n$ gravity is presented. We show that the cosmological equations can be written as a first order autonomous system and analyzed using the standard techniques of dynamical system theory. In absence of perfect fluid matter, we find exact solutions whose behavior and stability are analyzed in terms of the values of the parameter $n$. When matter is introduced, the nature of the (non-minimal) coupling between matter and higher order gravity induces restrictions on the allowed values of $n$. Selecting such intervals of values and following the same procedure used in the vacuum case, we present exact solutions and analyze their stability for a generic value of the parameter $n$. From this analysis emerges the result that for a large set of initial conditions an accelerated expansion is an attractor for the evolution of the $R^n$ cosmology. When matter is present a transient almost-Friedman phase can also be present before the transition to an accelerated expansion.

revised and extended version, 35 pages, 12 tables, 14 figures which are not included and can be found at http://www.mth.uct.ac.za/~peter/Rn

References in corpus (24)

• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• Type Ia Supernova Discoveries at z>1 From the Hubble Space Telescope: Evidence for Past Deceleration and Constraints on Dark Energy Evolution
• A Flat Universe from High-Resolution Maps of the Cosmic Microwave Background Radiation
• Is Cosmic Speed-Up Due to New Gravitational Physics?
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• Exponential potentials and cosmological scaling solutions
• Curvature Quintessence
• Brane-world gravity
• The Cosmology of Generalized Modified Gravity Models
• Curvature quintessence matched with observational data
• Where new gravitational physics comes from: M-theory?
• 1/R Curvature Corrections as the Source of the Cosmological Acceleration
• Consistent modified gravity: dark energy, acceleration and the absence of cosmic doomsday
• Cosmological implications of the MAXIMA-I high resolution Cosmic Microwave Background anisotropy measurement
• Palatini form of 1/R gravity
• Accelerating Cosmologies from S-Branes
• Higher order gravity theories and scalar tensor theories
• A Study of Accelerating Cosmologies from Superstring/M theories
• Accelerated Cosmological Models in First-Order Non-Linear Gravity
• Some aspects of the cosmological conformal equivalence between ``Jordan Frame'' and ``Einstein Frame''
• Inflation from M-Theory with Fourth-order Corrections and Large Extra Dimensions
• Phase-plane analysis of Friedmann-Robertson-Walker cosmologies in Brans-Dicke gravity
• Recovering the effective cosmological constant in extended gravity theories
• Qualitative properties of scalar-tensor theories of Gravity

Cited by in corpus (211)

• Dynamics of dark energy
• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Modified Gravity and Cosmology
• f(R) theories
• Extended Theories of Gravity
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• In the Realm of the Hubble tension $-$ a Review of Solutions
• Beyond the Cosmological Standard Model
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase
• Conditions for the cosmological viability of f(R) dark energy models
• Dynamical systems applied to cosmology: dark energy and modified gravity
• Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints
• Observational constraints on dark energy with generalized equations of state
• The Power of General Relativity
• f(R, T, R_μνT^μν) gravity phenomenology and ΛCDM universe
• Dynamics of Linear Perturbations in f(R) Gravity
• The Newtonian Limit of F(R) gravity
• Energy conditions in f(R)-gravity
• Phantom crossing, equation-of-state singularities, and local gravity constraints in f(R) models
• Cosmography of f(R) gravity
• Dark matter as a geometric effect in f(R) gravity
• The stability of modified gravity models
• Spherical symmetry in $f(R)$-gravity
• Cosmological constraints on f(R) gravity theories within the Palatini approach
• Solar System experiments do not yet veto modified gravity models
• On the LCDM Universe in f(R) gravity
• Fourth order gravity: equations, history, and applications to cosmology
• The evolution of density perturbations in f(R) gravity
• Analysis of Rotation Curves in the framework of R^n gravity
• f(R) gravity theories in Palatini formalism: cosmological dynamics and observational constraints
• On the stability of the cosmological solutions in f(R,G) gravity
• Constraints on scalar-tensor models of dark energy from observational and local gravity tests
• The Newtonian limit at intermediate energies
• Stability of the Einstein static universe in f(R) gravity
• Classifying and avoiding singularities in the alternative gravity dark energy models
• Dynamical behavior in mimetic F(R) gravity
• Density perturbations in f(R) gravity theories in metric and Palatini formalisms
• Matter density perturbations in modified gravity models with arbitrary coupling between matter and geometry
• Cosmological Constraints on $f(G)$ Dark Energy Models
• Axially symmetric solutions in f(R)-gravity
• The phase space view of f(R) gravity
• The Existence of Godel, Einstein and de Sitter Universes
• Cosmological dynamics of mimetic gravity
• Exact solutions of f(R) gravity coupled to nonlinear electrodynamics
• f(R) Gravity with Torsion: The Metric-Affine Approach
• Further Exact Cosmological Solutions to Higher-Order Gravity Theories
• On Wormhole Throats in $f(R)$ Gravity Theory
• Cosmological dynamics of Scalar--Tensor Gravity
• Some remarks on the dynamical systems approach to fourth order gravity
• Dark energy exponential potential models as curvature quintessence
• Shear dynamics in Bianchi I cosmologies with R^n-gravity
• Spherically Symmetric Solutions to Fourth-Order Theories of Gravity
• On the co-existence of matter dominated and accelerating solutions in f(G)-gravity
• Can f(R) Modified Gravity Theories Mimic a LCDM Cosmology?
• Solar system constraints on R${}^n$ gravity
• Exact cosmological solutions of scale-invariant gravity theories
• Dynamics of the anisotropic Kantowsky-Sachs geometries in $R^n$ gravity
• Reconstruction of the Scalar-Tensor Lagrangian from a LCDM Background and Noether Symmetry
• Dynamics of f(R)-cosmologies containing Einstein static models
• The Existence of Einstein Static Universes and their Stability in Fourth order Theories of Gravity
• A dynamical system analysis of hybrid metric-Palatini cosmologies
• A new framework for studying spherically symmetric static solutions in f(R) gravity
• Beyond the perfect fluid hypothesis for dark energy equation of state
• Phase Space Analysis of the Accelerating Multi-fluid Universe
• Constraining $f(R)$ gravity by the Large Scale Structure
• The evolution of cosmological gravitational waves in f(R) gravity
• Rational approximations of $f(R)$ cosmography through Padé polynomials
• Dynamical systems analysis of anisotropic cosmologies in $R^n$-gravity
• Accelerating Universe in Modified Theories of Gravity
• Bounce Conditions in f(R) Cosmologies
• Modified first-order Horava-Lifshitz gravity: Hamiltonian analysis of the general theory and accelerating FRW cosmology in power-law F(R) model
• Gravitational lensing in fourth order gravity
• An analysis of the phase space of Horava-Lifshitz cosmologies
• Accelerated Cosmological Models in Modified Gravity tested by distant Supernovae SNIa data
• Curvature driven acceleration : a utopia or a reality ?
• Kinematic model-independent reconstruction of Palatini $f(R)$ cosmology
• Large Scale Structure Constraints for a Class of f(R) Theories of Gravity
• Cosmological dynamics of exponential gravity
• The cosmic snap parameter in f(R) gravity
• Noether Charge and Black Hole Entropy in Modified Theories of Gravity
• Dynamical analysis on $f(R,\mathcal{G})$ cosmology
• A general solution in the Newtonian limit of f(R)- gravity
• On Higher Order Gravities, Their Analogy to GR, and Dimensional Dependent Version of Duff's Trace Anomaly Relation
• Observational constraints on Gauss-Bonnet cosmology
• Dynamical system analysis for nonminimal torsion-matter coupled gravity
• On the possibility of blue tensor spectrum within single field inflation
• Consistency of $f(R)=\sqrt{R^2-R_0^2}$ Gravity with the Cosmological Observations in Palatini Formalism
• Unveiling the Dynamics of the Universe
• Bounce behaviour in Kantowski-Sachs and Bianchi Cosmologies
• F(R) gravity's rainbow and its Einstein counterpart
• Global gravitational instability of FLRW backgrounds - interpreting the dark sectors
• Dark energy: investigation and modeling
• Cosmic dynamics and qualitative study of Rastall model with spatial curvature
• FLRW metric $f(R)$ cosmology with a perfect fluid by generating integrals of motion
• A detailed analysis of structure growth in $f(R)$ theories of gravity
• Dynamical System Analysis of Cosmologies with Running Cosmological Constant from Quantum Einstein Gravity
• Cosmological dynamics of fourth order gravity: A compact view
• The Newtonian limit of metric gravity theories with quadratic Lagrangians
• Spherical inhomogeneous solutions of Einstein and scalar-tensor gravity: a map of the land
• The Raychaudhuri equation in homogeneous cosmologies
• A new approach to the analysis of the phase space of f(R)-gravity
• Galaxy-CMB Cross-Correlation as a Probe of Alternative Models of Gravity
• Qualitative study of anisotropic Rastall cosmologies
• Phase-space analysis of a class of k-essence cosmology
• Dynamics of a parametrized dark energy model in $f(R,T)$ gravity
• Optimising Baryon Acoustic Oscillation Surveys - I: Testing the concordance LCDM cosmology
• Probing the existence of the ZTF Casimir wormholes in the framework of $f(\mathcal{R})$ gravity
• Gravitational Waves in f(R) Gravity Power Law Model
• Cosmological dynamics of fourth order gravity with a Gauss-Bonnet term
• Compactifying the state space for alternative theories of gravity
• Conformal Transformations in Cosmology of Modified Gravity: the Covariant Approach Perspective
• Dynamical analysis of generalised $f(R,\mathcal{L})$ theories
• Cosmology of $f(R,\square R)$ gravity
• Emergent Universe from Energy-Momentum Squared Gravity
• Naked Singularity Formation In f(R) Gravity
• Searching for dynamical black holes in various theories of gravity
• A dynamical system approach to higher order gravity
• Phase space of modified Gauss-Bonnet gravity
• Chaplygin-gas Solutions of f(R) Gravity
• Analytical solutions in $R+q{R}^n$ cosmology from singularity analysis
• Cosmic acceleration in non-canonical scalar field model - An interacting scenario
• New class of hybrid metric-Palatini scalar-tensor theories of gravity
• Late-time acceleration and Phantom Divide Line Crossing with Non-minimal Coupling and Lorentz Invariance Violation
• R^n gravity and the chameleon
• The dynamics of Bianchi I universes in $R^n$ cosmologies with torsion
• Cosmological evolution, future singularities, Little Rip and Pseudo-Rip in viable f(R) theories and their scalar-tensor counterpart
• The dynamical viability of scalar-tensor gravity theories
• Crossing the Phantom Divide Line in a DGP-Inspired $F(R,\varphi )$-Gravity
• The fate of Schwarzschild-de Sitter Black Holes in $f(R)$ gravity
• Higher Powers in Gravitation
• Exact Friedmann Solutions in Higher-Order Gravity Theories
• Dynamical systems of modified Gauss-Bonnet gravity: cosmological implications
• Cosmography and large scale structure by f(R) gravity: new results
• Dynamical analysis of nonminimal coupled theories
• Stable super-inflating cosmological solutions in f(R)-gravity
• New class of generalized coupling theories
• Local Gravity Constraints and Power Law f(R) Theories
• On tidal forces in f(R) theories of gravity
• Thawing models in the presence of a generalized Chaplygin gas
• Modified theory of gravity and the history of cosmic evolution
• Dynamical equivalence of $f(R)$ gravity in Jordan and Einstein frames
• Dynamical system approach of non-minimal coupling in AdS/CFT cosmology
• Cosmological evolution with quadratic gravity and nonideal fluids
• Dynamical conditions and causal transport of dissipative spherical collapse in $f(R,T)$ gravity
• Cosmology in modified $f(\mathcal{G})$ gravity: a late time cosmic phenomena
• Cosmological perturbations in f(G) gravity
• Tabletop potentials for inflation from $f(R)$ gravity
• Integrable modified gravity cosmological models with an additional scalar field
• The post-Minkowskian limit of f(R)-gravity
• Vacuum Solution of a Linear Red-Shift Based Correction in $f(R)$ Gravity
• Cosmological Dynamics of Modified Gravity With a Non-minimal Curvature-matter Coupling
• A study of perturbations in scalar-tensor theory using 1+3 covariant approach
• A note on the dynamical system formulations in $f(R)$ gravity
• About matter and dark-energy domination eras in R^n gravity or lack thereof
• On Shear-free perturbations of f(R) gravity
• On multifluid perturbations in scalar-tensor cosmology
• Observational tests of a two parameter power-law class modified gravity in Palatini formalism
• De Sitter stability in quadratic gravity
• Invariant quantities of Scalar-Tensor Theories for stellar structure
• Dynamical properties of Bianchi-I spacetimes in $f(R)$ gravity
• Cosmological dynamics of magnetic Bianchi I in viable $f(R)$ models of gravity
• Dynamics of generalized tachyon field
• Power-law solutions and accelerated expansion in scalar-tensor theories
• Phase Space of Anisotropic $R^n$ Cosmologies
• Parametrizing the transition to the phantom epoch with Supernovae Ia and Standard Rulers
• Non minimally coupled condensate cosmologies: a phase space analysis
• A new approach to cosmological perturbations in f(R) models
• Dynamic properties of cyclic cosmologies
• Halting eternal acceleration with an effective negative cosmological constant
• Canonical Scalar Field Inflation with a Woods-Saxon Potential
• Weak gravitational lensing by compact objects in fourth order gravity
• Non-Singular Bouncing Model in Energy Momentum Squared Gravity
• Multifluid cosmology in f (G) gravity
• Cosmological dynamics in six-order gravity
• Can neutrino viscosity drive the late time cosmic acceleration?
• Reconstruction of the singularity-free $f(\mathcal{R})$ gravity via Raychaudhuri equations
• Covariant gauge invariant theory of Scalar Perturbations in $f(R)$-gravity: a brief review
• Constraints on a $f(R)$ gravity dark energy model with early scaling evolution
• Isotropic universe with almost scale-invariant fourth-order gravity
• Irrotational-fluid cosmologies in fourth-order gravity
• Perfect fluid solutions of Brans-Dicke and f(R)cosmology
• Global structure of Black Holes via dynamical system
• Reconstruction of f(R) gravity models from observations
• Gauge Issues in Extended Gravity and f(R) Cosmology
• New one-parametric extension of the Starobinsky inflationary model
• On analytical solutions of f(R) modified gravity theories in FLRW cosmologies
• A (varying power)-law modified gravity
• Matter power spectrum in a power-law $f(G)$ gravity
• Classification of Einstein equations with cosmological constant in warped product space-time
• Reconstruction of $f(R)$ lagrangian from a massive scalar field
• Bouncing Universe with a Nonminimally Coupled Scalar Field on a Moving Domain Wall
• Late-time power-law stages of cosmological evolution in teleparallel gravity with nonminimal coupling
• A comprehensive analysis of the compact phase space for Hu-Sawicki $f(R)$ dark energy models including spatial curvature
• Hawking radiation and thermodynamics of dynamical black holes in phantom dominated universe
• Asymptotic solutions in f(R)-gravity
• A model-independent compact dynamical system formulation for exploring bounce and cyclic cosmological evolutions in $f(R)$ gravity
• Perturbations of quasi-Newtonian universes in scalar-tensor gravity
• Cosmological Singularity and Power-Law Solutions in Modified Gravity
• Large-scale structure power spectrum from scalar-tensor gravity
• Exact analytical vacuum solutions of $R^n$-gravity model depending on two variables
• Radiative Corrections in the (Varying Power)-Law Modified Gravity
• Dynamical Systems Analysis of $f(R,L_m)$ Gravity Model
• Scalar-tensor baryogenesis: a scalar-tensor completion of gravitational baryogenesis
• Numerical solutions for the $f(R)$-Klein-Gordon system
• Asymptotically Schwarzschild solutions in $f(R)$ extension of general relativity
• Scheme of integration of vacuum $F(R)$ gravity in a travelling wave variable
• Cosmic hierarchy in $f(R)$ gravity
• On the structural stability of a simple cosmological model in $R+\alpha R^2$ theory of gravity
• On inflationary parameters in scalar-tensor theories