Solar System tests in Brans–Dicke and Palatini $$f({\mathcal {R}})$$-theories

We compare Mercury’s precession test in standard general relativity, Brans–Dicke theories (BD), and Palatini $$f({\mathcal {R}})$$ f ( R ) -theories. We avoid post-Newtonian approximation and compute exact precession in these theories. We show that the well-known mathematical equivalence between Palatini $$f({\mathcal {R}})$$ f ( R ) -theories and a specific subset of BD theories does not extend to a really physical equivalence among theories since equivalent models still allow a different incompatible precession for Mercury depending on the solution one chooses. As a result one cannot use BD equivalence to rule out Palatini $$f({\mathcal {R}})$$ f ( R ) -theories. On the contrary, we directly discuss that Palatini $$f({\mathcal {R}})$$ f ( R ) -theories can (and specific models do) easily pass Solar System tests as Mercury’s precession.