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

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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.

Most cited references7

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A Parameterized Post-Friedmann Framework for Modified Gravity

(2007)
We develop a parameterized post-Friedmann (PPF) framework which describes three regimes of modified gravity models that accelerate the expansion without dark energy. On large scales, the evolution of scalar metric and density perturbations must be compatible with the expansion history defined by distance measures. On intermediate scales in the linear regime, they form a scalar-tensor theory with a modified Poisson equation. On small scales in dark matter halos such as our own galaxy, modifications must be suppressed in order to satisfy stringent local tests of general relativity. We describe these regimes with three free functions and two parameters: the relationship between the two metric fluctuations, the large and intermediate scale relationships to density fluctuations and the two scales of the transitions between the regimes. We also clarify the formal equivalence of modified gravity and generalized dark energy. The PPF description of linear fluctuation in f(R) modified action and the Dvali-Gabadadze-Porrati braneworld models show excellent agreement with explicit calculations. Lacking cosmological simulations of these models, our non-linear halo-model description remains an ansatz but one that enables well-motivated consistency tests of general relativity. The required suppression of modifications within dark matter halos suggests that the linear and weakly non-linear regimes are better suited for making complementary test of general relativity than the deeply non-linear regime.
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Solar system and equivalence principle constraints on f(R) gravity by chameleon approach

We study constraints on f(R) dark energy models from solar system experiments combined with experiments on the violation of equivalence principle. When the mass of an equivalent scalar field degree of freedom is heavy in a region with high density, a spherically symmetric body has a thin-shell so that an effective coupling of the fifth force is suppressed through a chameleon mechanism. We place experimental bounds on the cosmologically viable models recently proposed in literature which have an asymptotic form f(R)=R-lambda R_c [1-(R_c/R)^{2n}] in the regime R >> R_c. From the solar-system constraints on the post-Newtonian parameter gamma, we derive the bound n>0.5, whereas the constraints from the violations of weak and strong equivalence principles give the bound n>0.9. This allows a possibility to find the deviation from the LambdaCDM cosmological model. For the model f(R)=R-lambda R_c(R/R_c)^p with 0
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The Cosmology of f(R) Gravity in the Metric Variational Approach

(2007)
We consider the cosmologies that arise in a subclass of f(R) gravity with f(R)=R+\mu ^{2n+2}/(-R)^{n} and -1
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Author and article information

Journal
31 October 2008
2009-01-14
10.1103/PhysRevD.79.024009
0810.5664

WU-AP/295/08
Phys.Rev.D79:024009,2009
9 pages, 9 figures, v2: minor modifications, version accepted for publication in Phys. Rev. D
astro-ph gr-qc hep-th