Refracted Gravity And Superfluid Dark Matter

By audience demand and for ease of reference purposes. Refracted gravity is a newish gravity based approach to explaining dark matter phenomena.  Fuller analysis will come later. Some first impressions: 

(1) the shape of the matter distribution doesn't seem to be important and it doesn't seem to have a source of isotropy violation, which are both problematic; 

(2) like GR with a cosmological constant and many other gravity modifications, it is a scalar-tensor theory (Deur's GR-SI is a pure tensor theory as is GR without a cosmological constant) - an important downside of a scalar-tensor v. a tensor theory is that it makes generalization to a quantum gravity theory harder; 

(3) unlike Deur's approach, it doesn't appear to resolve the conservation of energy issues associated with the lion's share of gravity theories with a dark energy component, but this calls for closer inspection and isn't entirely clear from the abstract; 

(4) further inspection of the permittivity-mass density relationship proposed is necessary for me to really understand it; 

(5) it appears to have one more experimentally fixed parameter than GR with a cosmological constant, similar to relativistic MOND with a cosmological constant; 

(6) there are lots of key areas (early galaxy formation, CMB peaks, cluster dynamics, Bullet cluster, cluster collision rate expectations, tendency of satellite galaxies to line up in planes, Hubble tension) where it isn't clear what is predicted although other papers may develop the theory more fully;

(7) all development of gravity based solutions to dark matter and dark energy phenomena are a welcome change, even though I'm skeptical that this will get the job done and the core assumption about permittivity isn't very well motivated (at least in the abstract).

We propose a covariant formulation of refracted gravity (RG), a classical theory of gravity based on the introduction of the gravitational permittivity -- a monotonic function of the local mass density -- in the standard Poisson equation. 

The gravitational permittivity mimics the dark matter phenomenology. Our covariant formulation of RG (CRG) belongs to the class of scalar-tensor theories, where the scalar field φ has a self-interaction potential (φ)=−Ξφ, with Ξ a normalization constant. We show that the scalar field is twice the gravitational permittivity in the weak-field limit. 

Far from a spherical source of density ρs(r), the transition between the Newtonian and the RG regime appears below the acceleration scale aΞ=(2Ξ−8πGρ/φ)1/2, with ρ=ρs+ρbg and ρbg an isotropic and homogeneous background. 

In the limit 2Ξ≫8πGρ/φ, we obtain aΞ∼10−10~m~s−2. This acceleration is comparable to the acceleration a0 originally introduced in Modified Newtonian Dynamics (MOND). 

From CRG, we also derive the modified Friedmann equations for an expanding, homogeneous, and isotropic universe. We find that the same scalar field that mimics dark matter also drives the accelerated expansion of the Universe. Since Ξ plays a role roughly similar to the cosmological constant Λ in the standard model and has a comparable value, CRG suggests a natural explanation of the known relation a0∼Λ1/2. 

CRG thus appears to describe both the dynamics of cosmic structure and the expanding Universe with a single scalar field, and falls within the family of models that unify the two dark sectors, highlighting a possible deep connection between phenomena currently attributed to dark matter and dark energy separately.

Andrea Pierfrancesco Sanna, Titos Matsakos, Antonaldo Diaferio, "Covariant Formulation of refracted gravity" arXiv:2109.11217 (September 25, 2021) (submitted to Physical Review D).

A new paper on a superfluid dark matter theory with two of my favorite physicists as authors, which is betwixt and between a gravitational and a dark matter particle approach, finds that SFDM falls short. Again, any work on gravitational or MOND-replicating theories is a good thing, even if individual theory failures point the way to the true solution.

We investigate superfluid dark matter (SFDM), a model that promises to reproduce the successes of both particle dark matter on cosmological scales and those of Modified Newtonian Dynamics (MOND) on galactic scales. 

But SFDM reproduces MOND only up to a certain distance from the galactic center and only for kinematic observables. Most importantly, it does not affect trajectories of light. We test whether or not this is in conflict with a recent analysis of weak gravitational lensing which has probed accelerations around galaxies at unprecedentedly large radii. This analysis found the data to be close to the prediction of MOND, suggesting they might be difficult to fit with SFDM. 

To investigate this matter, we solved the equations of motion of the model and compared the result to observational data. Our results show that the SFDM model is incompatible with the weak-lensing observations, at least in its current form.

Tobias Mistele, Stacy McGaugh, Sabine Hossenfelder, "Superfluid dark matter in tension with weak gravitational lensing data" arXiv:2303.08560 (March 15, 2023).