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

TL;DR

This paper explores linearized scalar-tensor gravity theories with a cosmological term, analyzing their effects on solar system phenomena and galactic dynamics, and finds that large Brans-Dicke parameters make these theories behave like general relativity.

Contribution

It introduces two generalized scalar-tensor models with cosmological terms and derives their solutions, analyzing their observational implications in the solar system and beyond.

Findings

Cosmological constant has negligible effects on perihelion and light deflection in these theories.

Large Brans-Dicke parameter values make the theories' predictions converge to general relativity.

Scalar field mass influences the relevance of modifications at different scales.

Abstract

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. Geodesics of these solutions are also presented and solar system effects such as the advance of the perihelion, deflection of light rays and gravitational redshift were discussed. In general relativity cosmological constant has no role on these phenomena. We see that for the Brans-Dicke theory the cosmological constant has also no effect on these phenomena. This is because solar system observations require very large values of the Brans-Dicke parameter and the correction terms to these phenomena becomes identical to GR for these large values of this parameter. This result is also observed for the theory with arbitrary potential if the mass of the scalar field is very light. For a very heavy scalar field, however, there is no such limit on the value of this parameter and there are ranges of this parameter where these contributions may become relevant in these scales. Galactic and intergalactic dynamics is also discussed for these theories at the latter part of the paper with similar conclusions.