Stiff Matter Solution in Brans-Dicke Theory and The General Relativity Limit

Abstract

Generally the Brans-Dicke theory reduces to General Relativity in the limit $\omega \to \infty$ if the scalar field goes as $\varphi \propto 1/\omega$. However, it is also known that there are examples with $\varphi \propto 1/\sqrt{\omega }$ that does not tend to GR. We discuss another case: a homogeneous and isotropic universe filled with stiff matter. The power of time dependence of these solutions do not depend on $\omega$, and there is no General Relativity limit even though we have $\varphi \propto 1/\omega$. A perturbative analysis of this exotic case is carried out.

Reviewed version. Submitted to IJMPD