Tests del Sistema Solare in teorie di Brans-Dicke e Palatini f(R)

My thesis work consists, in the first place, in introducing the theories of Brans-Dicke and Palatini f(R) as Extended Theories of Gravitation, secondly, in performing the exact calculation of the Mercury's orbit precession test in Brans-Dicke theory and showing the dynamical equivalence of Palatini f(R)-theories with a subclass of Brans-Dicke theories which coincides with a degenerate set of theories. In view of degeneracy, one needs to add a potential which in fact establishes equivalence with Palatini f(R)-theories. For Brans-Dicke theories, the generic case and the degenerate one needs to be analysed separately. The non-degenerate case reproduces the results in literature, through by semi-analytical methods which are valid in the strong regime. Furthermore, the equivalence between Palatini f(R)-theories and General Relativity with cosmological constant is shown and the test of the precession of Mercury's orbit in a specific Palatini f(R)-theory based on the function f(R)=α R-β/2 R^2 -γ/3 R^(-1) is performed. In a previous paper it was discussed how SNIa data fixed a constraint on the parameters of the f(R). Here it is shown how the Solar System test produces an additional constraint. In particular, it is shown how one can have α quite different from α=1, as predicted by SNIa and still pass the Solar System test, provided that the ratio (γ/α)^(1/2), which plays the role of an effective cosmological constant, is kept constant and small enough. It is also discussed how other Solar System tests can further constrain the f(R).