5 Local Gravity Constraints

In this section we discuss the compatibility of f (R) models with local gravity constraints (see [469Jump To The Next Citation Point470Jump To The Next Citation Point245Jump To The Next Citation Point233Jump To The Next Citation Point154Jump To The Next Citation Point448Jump To The Next Citation Point251Jump To The Next Citation Point] for early works, and [31Jump To The Next Citation Point306Jump To The Next Citation Point134Jump To The Next Citation Point] for experimental constraints on viable f (R) dark energy models, and [101Jump To The Next Citation Point210330Jump To The Next Citation Point332Jump To The Next Citation Point471Jump To The Next Citation Point628Jump To The Next Citation Point14962532945511Jump To The Next Citation Point27753413344530989] for other related works). In an environment of high density such as Earth or Sun, the Ricci scalar R is much larger than the background cosmological value R0. If the outside of a spherically symmetric body is a vacuum, the metric can be described by a Schwarzschild exterior solution with R = 0. In the presence of non-relativistic matter with an energy density ρm, this gives rise to a contribution to the Ricci scalar R of the order κ2 ρm.

If we consider local perturbations δR on a background characterized by the curvature R0, the validity of the linear approximation demands the condition δR ≪ R0. We first derive the solutions of linear perturbations under the approximation that the background metric (0) gμν is described by the Minkowski metric ημν. In the case of Earth and Sun the perturbation δR is much larger than R0, which means that the linear theory is no longer valid. In such a non-linear regime the effect of the chameleon mechanism [344Jump To The Next Citation Point343Jump To The Next Citation Point] becomes important, so that f (R) models can be consistent with local gravity tests.

 5.1 Linear expansions of perturbations in the spherically symmetric background
 5.2 Chameleon mechanism in f (R) gravity
  5.2.1 Field profile of the chameleon field
  5.2.2 Thin-shell solutions
  5.2.3 Post Newtonian parameter
  5.2.4 Experimental bounds from the violation of equivalence principle
  5.2.5 Constraints on model parameters in f (R) gravity

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