# Dark range of $\omega$ in Brans-Dicke gravity

## TL;DR

This paper explores the behavior of the Brans-Dicke scalar-tensor theory of gravity, especially focusing on the negative range of the parameter , and investigates the scalar field  as a potential dark energy candidate in a gravitational wave context.

## Contribution

It presents the variational field equations of Brans-Dicke theory in both Riemannian and non-Riemannian frameworks using exterior differential forms, and analyzes test mass motion in Rosen coordinates for negative  values.

## Key findings

- Scalar field  may serve as dark energy for  in (-3/2, 0) range.
- Field equations derived in both Riemannian and non-Riemannian settings.
- Test mass motion analyzed in gravitational plane wave background.

## Abstract

The variational field equations of Brans-Dicke scalar-tensor theory of gravitation are presented in a Riemannian and non-Riemannian setting in the language of exterior differential forms over 4-dimensional spacetime. In Rosen coordinates, the equations of motion of non-spinning test masses are considered in a gravitational plane wave setup and detailed to interpret a scalar field $\alpha$ as a candidate for dark energy for negative values of the Brans-Dicke parameter $-3/2 < \omega < 0$ .