Boson Stars in the Brans-Dicke Gravitational Theories

Boson stars consist of a system of self-gravitating scalar fields which form a macroscopic quantum state and are a possible dark matter candidate. In this paper, we address the existence of boson stars in Brans-Dicke gravity. We show that solutions to the equations of motion of a boson star in Brans-Dicke gravity exist for different values of the coupling constant $\Lambda=\lambda M_{Pl}^2/4\pi m^2$, where $\lambda$ is the quartic coupling, and $m$ the mass of the boson field. We find that there is only a small decrease of a few percent in the mass of these objects when compared to similar solutions based on general relativity. We also consider solutions in the limit as $\Lambda \rightarrow\infty$.