Can f(R) Modified Gravity Theories Mimic a LCDM Cosmology?

Abstract

We consider f(R) modified gravity theories in the metric variation formalism and attempt to reconstruct the function f(R) by demanding a background LCDM cosmology. In particular we impose the following requirements: a. A background cosmic history H(z) provided by the usual flat LCDM parametrization though the radiation (w_eff=1/3), matter (w_eff=0) and deSitter (w_eff=-1) eras. b. Matter and radiation dominate during the `matter' and `radiation' eras respectively i.e. Ω_m =1 when w_eff=0 and Ω_r=1 when w_eff=1/3. We have found that the cosmological dynamical system constrained to obey the LCDM cosmic history has four critical points in each era which correspondingly lead to four forms of f(R). One of them is the usual general relativistic form f(R)=R-2Λ. The other three forms in each era, reproduce the LCDM cosmic history but they do not satisfy requirement b. stated above. Only one of these forms (different from general relativity) is found to be an attractor of the dynamical cosmological evolution. It has (Ω_DE=1, Ω_r=0, Ω_m=0) throughout the evolution. Its phase space trajectory is numerically obtained.

Minor Modifications. Accepted in Phys. Rev. D (to appear). 11 revtex pages, 6 figures. The mathematica files with the numerical analysis of the paper can be found at http://leandros.physics.uoi.gr/frlcdm/frlcdm.htm

References in corpus (25)

• Dynamics of dark energy
• Cosmology and the Fate of Dilatation Symmetry
• Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe
• 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
• Are f(R) dark energy models cosmologically viable ?
• Solar System constraints to general f(R) gravity
• The Cosmology of f(R) Gravity in the Metric Variational Approach
• Metric-affine f(R) theories of gravity
• The holographic dark energy in non-flat Brans-Dicke cosmology
• Dark Energy: the equation of state description versus scalar-tensor or modified gravity
• Matter instability in modified gravity
• The (pseudo)issue of the conformal frame revisited
• Stability of Cosmological Solution in f(R) Models of Gravity
• f(R) gravity theories in Palatini formalism: cosmological dynamics and observational constraints
• The acceleration of the universe and the physics behind it
• Ghosts, Instabilities, and Superluminal Propagation in Modified Gravity Models
• Viability of f(R) Theories with Additional Powers of Curvature
• Modified gravity as an alternative for Lambda-CDM cosmology
• Interacting dark energy in $f(R)$ gravity
• Late acceleration and $w=-1$ crossing in induced gravity
• Curvature scalar instability in f(R) gravity
• The Limits of Extended Quintessence
• The cosmic snap parameter in f(R) gravity
• Dark energy from bulk matter

Cited by in corpus (40)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• Modified f(R) gravity unifying R^m inflation with \LambdaCDM epoch
• Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints
• Energy conditions in f(R)-gravity
• The future evolution and finite-time singularities in $F(R)$-gravity unifying the inflation and cosmic acceleration
• A parametric model for dark energy
• Constraints on scalar-tensor models of dark energy from observational and local gravity tests
• Cosmological Constraints on f(R) Acceleration Models
• Density perturbations in f(R) gravity theories in metric and Palatini formalisms
• Aspects of cosmological expansion in F(R) gravity models
• Dark energy, inflation and dark matter from modified F(R) gravity
• Initial and final de Sitter universes from modified $f(R)$ gravity
• The Cosmology of Ricci-Tensor-Squared Gravity in the Palatini Variational Approach
• Finite-time Cosmological Singularities and the Possible Fate of the Universe
• Delicate f(R) gravity models with disappearing cosmological constant and observational constraints on the model parameters
• An overview of what current data can (and cannot yet) say about evolving dark energy
• The Cauchy problem of f(R) gravity
• Accelerating Universe in Modified Theories of Gravity
• Black hole entropy in modified gravity models
• Connecting early and late universe by $f(R)$ gravity
• Noether Charge and Black Hole Entropy in Modified Theories of Gravity
• Homogeneous cosmologies in generalized modified gravity
• Estimation of Cosmological Parameters, Stability Analysis and Energy Conditions in Viable Modified Gravity
• Future dynamics in f(R) theories
• Late Time Cosmological Evolution in f(R) theories with Ordinary and Collisional Matter
• Addressing Cosmological Tensions by Non-Local Gravity
• Cosmological dynamics of magnetic Bianchi I in viable $f(R)$ models of gravity
• Number Counts and Dynamical Vacuum Cosmologies
• Effective gravitational equations on brane world with induced gravity described by $f(R)$ term
• Stability analysis in Modified Non-Local Gravity
• Reconstructing a Model for Gravity at Large Distances from Dark Matter Density Profiles
• On the uniqueness of $\Lambda$CDM-like evolution for homogeneous and isotropic cosmology in General Relativity
• On Friedmann-Lema\^ıtre-Robertson-Walker cosmologies in non-standard gravity
• Investigation of Bouncing Universe and Phantom Crossing in Modified Gravity Coupled with Weyl Tensor and its Reconstruction
• A Unified Dynamical Systems Framework for Cosmology in $f(Q)$ Gravity: Generic Features Beyond the Coincident Gauge
• Matter Creation Cosmologies and Accelerated Expansion
• f(R) cosmological solutions with varying speed of light
• CLASH-VLT: The Fifth Force in Chameleon Gravity from Joint Lensing and Kinematics Cluster Mass Profiles