Study of Antigravity in an F(R) Model and in Brans-Dicke Theory with Cosmological Constant

We study antigravity, that is having an effective gravitational constant with a negative sign, in scalar-tensor theories originating from \(F(R)\)-theory and in a Brans-Dicke model with cosmological constant. For the \(F(R)\) theory case, we obtain the antigravity scalar-tensor theory in the Jordan frame by using a variant of the Lagrange multipliers method and we numerically study the time dependent effective gravitational constant. As we shall demonstrate by using a specific \(F(R)\) model, although there is no antigravity in the initial model, it might occur or not in the scalar-tensor counterpart, mainly depending on the parameter that characterizes antigravity. Similar results hold true in the Brans-Dicke model.