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.

10.1 Brans–Dicke theory and the equivalence with f (R) theories

10.2 Cosmological dynamics of dark energy models based on Brans–Dicke theory

10.3 Local gravity constraints

10.4 Evolution of matter density perturbations

10.2 Cosmological dynamics of dark energy models based on Brans–Dicke theory

10.3 Local gravity constraints

10.4 Evolution of matter density perturbations

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