Can the Brans-Dicke Gravity with $Λ$ Possibly be a Theory of Dark Matter?

Abstract

The pure Brans-Dicke (BD) gravity with or without the cosmological constant $Λ$ has been taken as a model theory for the dark matter. Indeed, there has been a consensus that unless one modifies either the standard theory of gravity, namely, general relativity, or the standard model for particle physics, or both, one can never achieve a satisfying understanding of the phenomena associated with dark matter and dark energy. Along this line, our dark matter model in this work can be thought of as an attempt to modify the gravity side alone in the simplest fashion to achieve the goal. Among others, it is demonstrated that our model theory can successfully predict the emergence of dark matter halo-like configuration in terms of a self-gravitating spacetime solution to the BD field equations and reproduce the flattened rotation curve in this dark halo-like object in terms of the non-trivial energy density of the BD scalar field, which was absent in the context of general relativity where Newton's constant is strictly a ``constant'' having no dynamics. Our model theory, however, is not entirely without flaw, such as the prediction of relativistic jets in all types of galaxies which actually is not the case.