Can higher curvature corrections cure the singularity problem in f(R) gravity?

Abstract

Although $f(R)$ modified gravity models can be made to satisfy solar system and cosmological constraints, it has been shown that they have the serious drawback of the nonexistence of stars with strong gravitational fields. In this paper, we discuss whether or not higher curvature corrections can remedy the nonexistence consistently. The following problems are shown to arise as the costs one must pay for the $f(R)$ models that allow for neutrons stars: (i) the leading correction must be fine-tuned to have the typical energy scale $\mu \lesssim 10^{-19}$ GeV, which essentially comes from the free fall time of a relativistic star; (ii) the leading correction must be further fine-tuned so that it is not given by the quadratic curvature term. The second problem is caused because there appears an intermediate curvature scale and laboratory experiments of gravity will be under the influence of higher curvature corrections. Our analysis thus implies that it is a challenge to construct viable $f(R)$ models without very careful and unnatural fine-tuning.

9 pages, 9 figures, v2: minor modifications, version accepted for publication in Phys. Rev. D

References in corpus (48)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Type Ia Supernova Discoveries at z>1 From the Hubble Space Telescope: Evidence for Past Deceleration and Constraints on Dark Energy Evolution
• 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
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Chameleon Fields: Awaiting Surprises for Tests of Gravity in Space
• Chameleon Cosmology
• The Confrontation between General Relativity and Experiment
• Disappearing cosmological constant in f(R) gravity
• Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Can modified gravity explain accelerated cosmic expansion?
• 1/R gravity and Scalar-Tensor Gravity
• Unifying inflation with LambdaCDM epoch in modified f(R) gravity consistent with Solar System tests
• Do consistent $F(R)$ models mimic General Relativity plus $\Lambda$?
• 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
• Constraining f(R) Gravity as a Scalar Tensor Theory
• Evading Equivalence Principle Violations, Cosmological and other Experimental Constraints in Scalar Field Theories with a Strong Coupling to Matter
• Solar System constraints to general f(R) gravity
• The Cosmology of f(R) Gravity in the Metric Variational Approach
• f(R) Gravity and Chameleon Theories
• Consistent modified gravity: dark energy, acceleration and the absence of cosmic doomsday
• Solar system and equivalence principle constraints on f(R) gravity by chameleon approach
• Phantom crossing, equation-of-state singularities, and local gravity constraints in f(R) models
• The future evolution and finite-time singularities in $F(R)$-gravity unifying the inflation and cosmic acceleration
• Solar System tests DO rule out 1/R gravity
• A Singularity Problem with f(R) Dark Energy
• Strongly Coupled Chameleon Fields: New Horizons in Scalar Field Theory
• Relativistic stars in f(R) gravity, and absence thereof
• f(R) actions, cosmic acceleration and local tests of gravity
• Static spherically symmetric perfect fluid solutions in $f(R)$ theories of gravity
• Newton law corrections and instabilities in $f(R)$ gravity with the effective cosmological constant epoch
• The Newtonian limit at intermediate energies
• Local and Global Variations of The Fine Structure Constant
• Viability of f(R) Theories with Additional Powers of Curvature
• A no-go theorem for polytropic spheres in Palatini f(R) gravity
• Aspects of cosmological expansion in F(R) gravity models
• Inhomogeneous Gravity
• Spherically symmetric spacetimes in f(R) gravity theories
• Delicate f(R) gravity models with disappearing cosmological constant and observational constraints on the model parameters
• Curvature singularities, tidal forces and the viability of Palatini f(R) gravity
• Re-examination of Polytropic Spheres in Palatini f(R) Gravity
• Stellar configurations in f(R) theories of gravity
• Equilibrium hydrostatic equation and Newtonian limit of the singular f(R) gravity
• Constraining Newtonian stellar configurations in f(R) theories of gravity
• On the stability of spherically symmetric spacetimes in metric f(R) gravity

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