If the field potential is present, the models with large couplings () can be consistent with
local gravity constraints as long as the mass
of the field
is sufficiently large in the region of high
density. For example, the potential (10.23
) is designed to have a large mass in the high-density region so
that it can be compatible with experimental tests for the violation of equivalence principle through the
chameleon mechanism [596
]. In the following we study conditions under which local gravity constraints can
be satisfied for the model (10.23
).
As in the case of metric f (R) gravity, let us consider a configuration in which a spherically symmetric
body has a constant density inside the body with a constant density
outside the
body. For the potential
in the Einstein frame one has
under the
condition
. Then the field values at the potential minima inside and outside the body are
Recall that is roughly the same order as the present cosmological density
. The
baryonic/dark matter density in our galaxy corresponds to
. The mean density of Sun
or Earth is about
. Hence
and
are in general much larger than
for
local gravity experiments in our environment. For
the chameleon mechanism we discussed in
Section 5.2 can be directly applied to BD theory whose Einstein frame action is given by Eq. (10.6
) with
.
The bound (5.56) coming from the possible violation of equivalence principle in the solar system
translates into
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