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 [100] 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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