Antigravity in F(R) and Brans-Dicke theories

We study antigravity in F ( R )-theory originating scalar-tensor theories and also in Brans-Dicke models without cosmological constant. For the F ( R ) theory case, we obtain the Jordan frame antigravity scalar-tensor theory by using a variant of the Lagrange multipliers method and we numerically study the time dependent effective gravitational constant. As we shall demonstrate in detail by using some viable F ( R ) models, although the initial F ( R ) models have no antigravity, their scalar-tensor counterpart theories might or not have antigravity, a fact mainly depending on the parameter that characterizes antigravity. Similar results hold true in the Brans-Dicke model, which we also studied numerically. In addition, regarding the Brans-Dicke model we also found some analytic cosmological solutions. Since antigravity is an unwanted feature in gravitational theories, our findings suggest that in the case of F ( R ) theories, antigravity does not occur in the real world described by the F ( R ) theory, but might occur in the Jordan frame scalar-tensor counterpart of the F ( R ) theory, and this happens under certain circumstances. The central goal of our study is to present all different cases in which antigravity might occur in modified gravity models.