Linearized modified gravity theories with a cosmological term: advance of perihelion and deflection of light

Understand

Two different ways of generalizing Einstein's general theory of relativity with a cosmological constant to Brans-Dicke type scalar-tensor theories are investigated in the linearized field approximation.

• In the first case a cosmological constant term is coupled to a scalar field linearly whereas in the second case an arbitrary potential plays the role of a variable cosmological term.
• We see that the former configuration leads to a massless scalar field whereas the latter leads to a massive scalar field.
• General solutions of these linearized field equations for both cases are obtained corresponding to a static point mass.