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

TL;DR

This paper explores a unique stiff matter solution in Brans-Dicke theory that does not approach General Relativity in the limit, highlighting an exception to the usual convergence behavior.

Contribution

It presents a new class of solutions with constant time dependence power that defy the typical GR limit in Brans-Dicke theory.

Findings

Solution's time dependence is independent of ω

No GR limit despite φ∝1/ω

Perturbative analysis confirms the exotic behavior

Abstract

Generally the Brans-Dicke theory reduces to General Relativity in the limit $\omega\rightarrow\infty$ if the scalar field goes as $\phi\propto1/\omega$. However, it is also known that there are examples with $\phi\propto1/\sqrt{\omega}$ 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 $\phi\propto1/\omega$. A perturbative analysis of this exotic case is carried out.