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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 will 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

journal of gravity

Study of Antigravity in an <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>F</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> Model and in Brans-Dicke Theory with Cosmological Constant

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