In this section we discuss the compatibility of f (R) models with local gravity
constraints (see [469, 470
, 245
, 233
, 154
, 448
, 251
] for early works, and [31
, 306
, 134
] for experimental constraints on
viable f (R) dark energy models, and [101
, 210, 330
, 332
, 471
, 628
, 149, 625, 329, 45, 511
, 277, 534, 133, 445, 309, 89]
for other related works). In an environment of high density such as Earth or Sun, the Ricci scalar
is
much larger than the background cosmological value
. If the outside of a spherically symmetric body is
a vacuum, the metric can be described by a Schwarzschild exterior solution with
. In the presence of
non-relativistic matter with an energy density
, this gives rise to a contribution to the Ricci scalar
of the order
.
If we consider local perturbations on a background characterized by the curvature
, the
validity of the linear approximation demands the condition
. We first derive the solutions of
linear perturbations under the approximation that the background metric
is described by the
Minkowski metric
. In the case of Earth and Sun the perturbation
is much larger than
,
which means that the linear theory is no longer valid. In such a non-linear regime the effect of the
chameleon mechanism [344
, 343
] becomes important, so that f (R) models can be consistent with local
gravity tests.
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