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

TL;DR

This paper investigates the conditions under which antigravity, characterized by a negative effective gravitational constant, can occur in scalar-tensor theories derived from $F(R)$-theory and Brans-Dicke models, using numerical analysis.

Contribution

It introduces a method to derive antigravity scalar-tensor theories from $F(R)$ models and analyzes the parameter dependence of antigravity emergence in these theories.

Findings

Antigravity can develop in scalar-tensor theories even if absent in the original $F(R)$ model.

The occurrence of antigravity depends on specific parameters in the models.

Numerical studies show the effective gravitational constant can switch sign over time.

Abstract

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.