So far we have discussed f (R) gravity theories in the metric and Palatini formalisms. In this section we will see that these theories are equivalent to Brans–Dicke (BD) theory  in the presence of a scalar-field potential, by comparing field equations in f (R) theories with those in BD theory. It is possible to construct viable dark energy models based on BD theory with a constant parameter . We will discuss cosmological dynamics, local gravity constraints, and observational signatures of such generalized theory.
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