A Special Class of the Scalar-Tensor Gravity with Scalar-Matter Direct Coupling

TL;DR

This paper investigates how scalar-matter direct coupling influences the evolution of scalar-tensor gravity, revealing conditions under which it reduces to Einstein's gravity and how the attractor mechanism is affected.

Contribution

It introduces a new coupling strength parameter $eta$ and analyzes its impact on the attractor mechanism in scalar-tensor gravity models.

Findings

Scalar-matter coupling modifies the evolution equations.

The coupling strength $eta$ must be added to the master equation.

The attractor mechanism depends on the combined potential $ ext{ln}A( ext{varphi}) + ext{ln}C( ext{varphi})$.

Abstract

A role of the scalar-matter direct coupling in the evolution of scalar-tensor gravity was studied. If the coupling functions in the generalized scalar-tensor gravity satisfy a definite equation the scalar-tensor gravity is reduced to Einstein's tensor gravity. We consider the issue in Jordan frame and then Einstein frame. It is shown that the coupling strength in the right hand side of the master equation obtained in Damour and Nordtvedt(1993) must be added by a coupling strength $\hat{\beta}$ which characterizes the scalar-matter direct coupling. If a minimum of potential $\ln C(\varphi)$ does not coincide with one of the potential $\ln A(\varphi)$ or the potential $\ln C(\varphi)$ does not have any minimum and is a monotonic function, then the attractor mechanism of scalar-tensor gravity toward pure general relativity should be modified, and the combined potential $\ln A(\varphi)+\ln C(\varphi)$ will determine the attractor mechanism.