Gravitational Wave Solutions to Linearized Jordan-Brans-Dicke Theory on a Cosmological Background

TL;DR

This paper derives approximate vacuum solutions for linearized Jordan-Brans-Dicke theory on a cosmological background, revealing conditions for gravitational wave existence and implications for different omega values.

Contribution

It provides new solutions for perturbed scalar fields and metrics in Jordan-Brans-Dicke theory, especially at omega = -3/2, and explores their cosmological implications.

Findings

Solutions show scale factor proportional to t and scalar field proportional to t^{-2} at omega = -3/2.

Results indicate conditions for gravitational waves in vacuum within JBD theory.

Omega values influence conformal invariance and fit supernovae data.

Abstract

Approximate vacuum solutions of Jordan-Brans-Dicke theory for perturbed scalar field and perturbed Robertson-Walker metric, are found. Solutions for the scale factor and the scalar field in unperturbed JBD theory are dependent on the $\omega$ parameter which determines how the scalar field is coupled to geometry of space-time. After adding a metric perturbation to Robertson-Walker metric and a perturbation to the scalar field, we solved the linearized JBD equations and found the scale factor and the scalar field as $a\propto t$ and $\phi\propto t^{-2}$ with $\omega=$-3/2. The results are necessary conditions for ordinary and scalar gravitational waves to exist in the vacuum case. Despite omega is a large positive number for current solar system environment observations, this value of omega makes JBD theory conformally invariant and fits recent supernovae type Ia data. We also looked for the value of omega for the case which has nonzero spatial curvature parameter.