Gravitational wave solutions to linearized Jordan Brans Dicke theory on a cosmological background

Abstract

In this thesis, approximate vacuum solutions of Jordan-Brans-Dicke theory for perturbed scalar eld and perturbed Robertson-Walker metric, were found. First we obtained solutions for the scale factor a(t) and the scalar eld (t) in unperturbed JBD theory. The solutions are dependent on JBD constant !JBD which is the value of how the scalar eld is coupled to geometry of space-time. Then we added metric perturbation h (x) to Robertson-Walker metric and perturbation (x) to the scalar eld (t) in order to construct linearized JBD equations. After acquiring the metric perturbation and ( = ) as gravitational wave and scalar gravitational wave respectively, we solved the JBD equations which are rst order in h (x) and (x) such that the scale factor and the scalar eld solutions are a / t and / t{u100000}2 with !JBD = {u100000}3=2. These results are necessary conditions for ordinary and scalar gravitational waves to exist in vacuum case. Despite !JBD > 104 for current solar system environment observations, !JBD = {u100000}3=2 makes JBD theory conformally invariant and ts recent supernovae type Ia data.