>"explain galactic rotation curves without needing to evoke dark matter."
I wonder if this makes it incompatible with dark matter?
If stochastic spacetime explains the rotation curves exactly without black matter, then black matter can't exist at the same time.
The evidence for dark matter is find in, galaxy rotation curves, gravitational lensing, cosmic microwave background, structure formation, bullet cluster and other galaxy cluster collisions, baryon acoustic oscillations, Lyman-alpha forest absorption lines, etc.
There is plenty of evidence for dark matter and it's existence is widely accepted. Explaining just one piece of evidence can be evidence against the new explanation if it's incompatible.
> Can dark matter and [the author's theory of gravitation] fit together...?
Nobody knows yet. The authors aren't seeking to overthrow the concordance cosmology; this paper is essentially trying to see if their theory is quickly killed by being unable to model a stable spherically symmetric galaxy in an expanding universe. Their theory predicts significant differences from the Schwarzschild-de Sitter (SdS) metric in General Relativity, with SdS serving as a proxy for an isolated galaxy. The paper in part investigates whether those differences can be "hidden" by removing the cold dark matter which otherwise would be the standard source of outer orbit anomalies.
They don't go deeper than that, and at this stage just can't: "To make it tractable analytically, we have restricted ourselves to spherically symmetric and static spacetimes". They restrict themselves in other ways too.
> The evidence for dark matter
From just after Eqn (23) in the preprint:
"While this study demonstrates that galactic rotation curves can undergo modification due to stochastic fluctuations, a phenomenon attributed to dark matter, it is important to acknowledge the existence of separate, independent evidence supporting ΛCDM. In particular, in the CMB power spectrum, in gravitational lensing, in the necessity of dark matter for structure formation, and in a varied collection of other methods used to estimate the mass in galaxies"
It doesn't explain the rotation curves of galaxies at all, and doesn't try to.
It takes a simple proxy for an isolated galaxy and sees if there are physically reasonable orbits around it. MOND-like orbits are physically reasonable (we observe them). The authors' model allows for almost MOND-like orbits.
The explanation for why these MOND-like orbits exist will vary. In the standard cosmology, it's because of a distribution of cold dark matter around the central mass. In MOND, it's because the strength of Newtonian gravitation falls off at great range from the central mass. In the theory discussed above it's because the central mass induces fluctuations in the gravitational field that grow in relevance with distance from the central mass, and in a particular range of radial distances those fluctuations are most likely to drop the orbiting body onto a closer orbit.
I wonder if this makes it incompatible with dark matter? If stochastic spacetime explains the rotation curves exactly without black matter, then black matter can't exist at the same time.
The evidence for dark matter is find in, galaxy rotation curves, gravitational lensing, cosmic microwave background, structure formation, bullet cluster and other galaxy cluster collisions, baryon acoustic oscillations, Lyman-alpha forest absorption lines, etc.
There is plenty of evidence for dark matter and it's existence is widely accepted. Explaining just one piece of evidence can be evidence against the new explanation if it's incompatible.