Antigravity in F(R) and Brans-Dicke theories

Abstract

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.