A three-parameter model for dark matter halos based on general relativity and quantum field theory

In this paper, we present a three-parameter model for the distributions of “dark matter” around local spherically symmetric and static distributions of normal matter, usually referred to as “dark matter halos”. The model is based on the assumption that the spontaneous symmetry breaking mechanism involving the Higgs field in the standard model of elementary particle physics leads to the existence of a constant distribution of vacuum energy throughout space–time. This is to be interpreted as a constant distribution of proper energy, as measured by local observers in their proper reference frames. Due to the presence of this universal distribution of vacuum energy, the model requires the introduction of the cosmological term in the Einstein field equations, in order to regulate the behavior of the resulting geometry at cosmologically large distances. By implementing the model on galactic scales, we are able to establish the gravitational consequences of such a homogeneous distribution of proper energy density at these scales. This results in equivalent halo masses and orbital velocity curves that, at least qualitatively, match the observations for galactic “dark matter” halos. Although the detailed realization of the model presented and calculated here cannot be construed as a precise representation of galactic structure, given that most of the actual structure of the galaxy, such as the galactic disk itself, is ignored, and replaced by a single spherically symmetric bulge, in this paper we do introduce the conceptual framework that may be used to construct a more complete galactic model in the future.