Constraining Newtonian stellar configurations in f(R) theories of gravity

Abstract

We consider general metric $f(R)$ theories of gravity by solving the field equations in the presence of a spherical static mass distribution by analytical perturbative means. Expanding the field equations systematically in $\cO(G)$, we solve the resulting set of equations and show that $f(R)$ theories which attempt to solve the dark energy problem very generally lead to ${\gamma }_{PPN}=1/2$ in the solar system. This excludes a large class of theories as possible explanations of dark energy. We also present the first order correction to ${\gamma }_{PPN}$ and show that it cannot have a significant effect.

arXiv comment4 pages; v2: added references, modified abstract and introduction, conclusions unchanged

References in corpus (25)

• 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
• Curvature Quintessence
• Can modified gravity explain accelerated cosmic expansion?
• 1/R gravity and Scalar-Tensor Gravity
• The Cosmology of Generalized Modified Gravity Models
• One-loop f(R) gravity in de Sitter universe
• On Physical Equivalence between Nonlinear Gravity Theories
• Where new gravitational physics comes from: M-theory?
• Spherically symmetric solutions of modified field equations in f(R) theories of gravity
• The Power of General Relativity
• The conformal frame freedom in theories of gravitation
• The gravity lagrangian according to solar system experiments
• Limit to General Relativity in f(R) theories of gravity
• Accelerated Cosmological Models in Ricci squared Gravity
• Stability of Cosmological Solution in f(R) Models of Gravity
• The stability of modified gravity models
• Higher order gravity theories and scalar tensor theories
• Solar System experiments do not yet veto modified gravity models
• The Force of Gravity from a Lagrangian containing Inverse Powers of the Ricci Scalar
• Newton law corrections and instabilities in $f(R)$ gravity with the effective cosmological constant epoch
• Cosmological Evolution in 1/R-Gravity Theory
• Spherically symmetric spacetimes in f(R) gravity theories
• Post-Newtonian Parameters from Alternative Theories of Gravity
• Cosmological expansion and the uniqueness of gravitational action

Cited by in corpus (24)

• 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
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Future of the universe in modified gravitational theories: Approaching to the finite-time future singularity
• The future evolution and finite-time singularities in $F(R)$-gravity unifying the inflation and cosmic acceleration
• Relativistic stars in f(R) gravity, and absence thereof
• Thin accretion disks in f(R) modified gravity models
• Dark energy, inflation and dark matter from modified F(R) gravity
• Exact solutions of f(R) gravity coupled to nonlinear electrodynamics
• On Wormhole Throats in $f(R)$ Gravity Theory
• Initial and final de Sitter universes from modified $f(R)$ gravity
• Can higher curvature corrections cure the singularity problem in f(R) gravity?
• Delicate f(R) gravity models with disappearing cosmological constant and observational constraints on the model parameters
• Spherically symmetric black holes in $f(R)$ gravity: Is geometric scalar hair supported ?
• Revisiting chameleon gravity - thin-shells and no-shells with appropriate boundary conditions
• Spherical inhomogeneous solutions of Einstein and scalar-tensor gravity: a map of the land
• A no-hair theorem for spherically symmetric black holes in $R^2$ gravity
• Pressure effects in the weak-field limit of f(R) = R + alpha R^2 gravity
• Hamiltonian perturbation theory in f(R) gravity
• Consistency of $f(R)$ gravity models around solar polytropes