# Linearized modified gravity theories and gravitational waves physics in the GBD theory

## TL;DR

This paper investigates the linearized gravitational physics and gravitational wave properties of the generalized Brans-Dicke (GBD) theory, revealing its potential to resolve observational issues and exhibit additional gravitational wave modes beyond general relativity.

## Contribution

It extends the analysis of GBD theory by deriving linearized equations and solutions, demonstrating its consistency with observations and exploring its gravitational wave characteristics.

## Key findings

- The GBD theory can produce a PPN parameter $$ consistent with observations.
- Gravitational waves in GBD have additional modes beyond GR.
- The $$ parameter problem in $f(R)$ theories is addressed in GBD.

## Abstract

The generalized Brans-Dicke (abbreviated as GBD) theory is obtained by replacing the Ricci scalar $R$ in the original Brans-Dicke (BD) action with an arbitrary function $f(R)$. Comparing with other theories, some interesting properties have been found or some problems existing in other theories could be solved in the GBD theory. For example, (1) the state parameter of geometrical dark energy in the GBD model can cross over the phantom boundary $w=-1$, without bearing the problems existing in the quintom model (e.g. the problem of negative kinetic term and the fine-tuning problem, etc); (2) $f(R)$ theory is equivalent to the BD theory with a potential (BDV) with the couple parameter $\omega=0$, where the kinetic term of field in the equivalent BDV theory is absent. While the scalar fields in the GBD own the non-disappeared kinetic term, when one compares the GBD theory with the $f(R)$ theory. In this paper, we continue to investigate the GBD theory. Using the method of the weak-field approximation, we explore the linearized physics in the GBD theory. The linearized equations of the gravitational field and two scalar fields are given. We investigate their solutions in the linearized theory for a point mass. It is shown that the problem of the $\gamma$ (parametrized post-Newtonian parameter) value in the $f(R)$ theory could be solved in the GBD theory, where the theoretical $\gamma$ value in the GBD theory can be consistent with the observational results. At last, we study the gravitational waves physics in the vacuum for the GBD theory. It is found that the gravitational radiation in the GBD theory has new freedoms beyond the two standard modes in the general relativity theory.