Generally speaking, gravity modification theories are better explanations of dark matter phenomena than dark matter particle theories. In gravity modification theories (which sometimes have scalar and/or vector gravitons or massive gravitons in addition to massless tensor gravitons), gravitons are what give rise to dark matter phenomena.
The theories discussed in the pre-print below involve dark matter particles, nominally unrelated to gravity, that have wave-like behavior and per particle mass-energies reasonable close to those of gravitons in a vanilla quantum gravity realization of General Relativity or a modest modification of it. The convergence of dark matter particle theories on this class of dark matter particles, as astronomy observations increasingly rule out or disfavor the alternatives, is itself interesting.
The Scalar Field Dark Matter model has been known in various ways throughout its history; Fuzzy, BEC, Wave, Ultralight, Axion-like Dark Matter, etc.
All of them consist in proposing that the dark matter of the universe is a spinless field Φ that follows the Klein-Gordon (KG) equation of motion ◻Φ−dV/dΦ=0, for a given scalar field potential V. The difference between different models is sometimes the choice of the scalar field potential V.
In the literature we find that people usually work in the nonrelativistic, weak-field limit of the KG equation where it transforms into the Schrödinger equation and the Einstein equations into the Poisson equation, reducing the KG-Einstein system, to the Schrödinger-Poisson system.
In this paper, we review some of the most interesting achievements of this model from the historical point of view and its comparison with observations, showing that this model could be the last answer to the question about the nature of dark matter in the universe.
Tonatiuh Matos, Luis A. Ureña-López, Jae-Weon Lee, "Short Review of the main achievements of the Scalar Field, Fuzzy, Ultralight, Wave, BEC Dark Matter model" arXiv:2312.00254 (November 30, 2023).