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 . 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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