Dark Matter as Superfluid (Khoury)

[haushofer]

I have a question, but I'm not sure this is the right place. Justin Khoury has the hypothesis that MOND on galactic scales can be explained with a superfluid of dark matter. In such a superfluid the correlation length goes to infinity, implying a scale invariance (a "phase transition) which as a result (I'm not sure of the details yet) mediates the long range force which would act as "modified gravity". My question: does this scaling invariance have anything to do with the scaling invariance Milgrom introduces which explains the Tully-Fisher relation? See e.g.



and a bit more detail,



or

https://arxiv.org/abs/2109.10928

If this question should be asked in a separate topic, let me know.

 

[Vanadium 50]

My question: does this scaling invariance

Where does Khoury mention this? In his paper, I only find this in a description of another theory.

 

[haushofer]

Where does Khoury mention this? In his paper, I only find this in a description of another theory.

Afaik he doesn't: it's discussed e.g. here,

https://arxiv.org/abs/0810.4065

by Milgrom. But as I understand, with a phase transition like superfluidity the correlation length goes to infinity, giving effectively a conformal field theory (in gauge theories these massless modes become the transverse polarization modes of the gauge vector bosons), so I was wondering whether Milgroms scaling 'emergent' symmetry of spacetime can be understood as the same scaling symmetry characterizing the phase transition of the dark matter fluid.

 

[Vanadium 50]

Afaik he doesn't

Then what is there to discuss about it? Milgrom obviously was unaware of Khoury's work when he wrote his paper, as it was more than a decade earlier.

 

[haushofer]

Then what is there to discuss about it? Milgrom obviously was unaware of Khoury's work when he wrote his paper, as it was more than a decade earlier.

What I said: is Milgrom's proposal of scale invariance in any way connected to Khoury's proposal of DM as a superfluid in which the correlation length becomes infinitely large?

As I understand it, conformal symmetries emerge during phase transitions. In MOND a scaling symmetry ('nonrelativistic conformal symmetry) emerges. So my question is whether there is a connection, explaining that MOND emerges out of Khoury's superfluid.

 

[mitchell porter]

I find "Theory of Dark Matter Superfluidity" (2015) by Berezhiani and Khoury, to be their most useful paper. In that paper, not only do they cite the "unitary Fermi gas" of Son and Wingate (2005) as a precedent, but in part 6, they actually give an example of a scalar field theory that gives a condensate with their MOND equation of state.

The paradigm shared with the unitary Fermi gas, is one of a conformal symmetry that is spontaneously broken. The work from Milgrom that they cite is not "The MOND limit from space-time scale invariance" (2008), but an earlier Milgrom paradigm, "Forces in Nonlinear Media" (2002), which is obscure enough that Milgrom doesn't even cite it in his own review of MOND for Scholarpedia.

Milgrom has considered a lot of approaches to MOND over the years. Tentatively I suggest that you could think about this case, in terms of two approaches to "modified Poisson gravity", what I'll call the geometric and the condensed matter approaches. Milgrom (2008) is an example of the geometric approach, it interprets the emergent conformal symmetry as a space-time symmetry. In the condensed matter approach, it doesn't. Berezhiani and Khoury's superfluid is one example of this; another would be Blanchet's dipolar dark matter, in which MOND comes from a gravitational version of the dielectric effect.

 

[Vanadium 50]

What you actually said was

Justin Khoury has the hypothesis that MOND on galactic scales can be explained with a superfluid of dark matter. In such a superfluid the correlation length goes to infinity, implying a scale invariance (a "phase transition)

And I am trying to figure out where he said anything about a scale invariance. MOND is manifestly not scale invariant, as it has a parameter of m/s² as a fundamental parameter. So I am trying to understand what you mean.

If you are saying that Milgrom made some suppositions, and maybe Khory's publications support them (but does not say so explicitly), well, maybe. But I think you need a lot more connecting-of-the-dots to get people on the same page. That would almost be a research paper in its own right.

 

[strangerep]

MOND is manifestly not scale invariant, as it has a parameter of m/s² as a fundamental parameter.

MOND becomes spacetime scale invariant in the so-called deep-MOND regime, i.e., where $|a| \ll a_0$.

If you are saying that Milgrom made some suppositions, and maybe Khory's publications support them (but does not say so explicitly), well, maybe. But I think you need a lot more connecting-of-the-dots to get people on the same page. That would almost be a research paper in its own right.

Indeed. But like @haushofer I've also wondered where/whether these other models (a.k.a Einstein-Aether, Aether-Scalar-Tensor, or distinguished superfluidic vector field), which claim to reproduce MOND phenomenlogy (or at least, some of it) in some limit or circumstances, also exhibit scaling invariance in that limit. The theories of Hossenfelder+Mistele and Zlosnik et al are also of this type (iiuc), but (also iiuc) the most recent analyses of Mistele, McGaugh & Hossfelder here are not encouraging.

Hmm, I just noticed Mistele's paper on certain limits in AeST theory where he tries to investigate this.

 

[haushofer]

For my PhD-thesis I constructed different theories of gravity by gauging the underlying Lie algebras describing the spacetime symmetries. It's been a while, but I'd expect that there are not that many extensions of the Bargmann algebra containing the scale symmetry as mentioned by Milgrom. Natural extensions like the Schrödinger algebra (https://arxiv.org/abs/1409.5555) or Galilean conformal algebra (https://arxiv.org/abs/0902.1385) don't scale space and time in a similar way, i.e. scale with z = 2 instead of z = 1 (and the gauging procedure fails for the Galilean conformal algebra anyway). This z = 1 scaling is typical of relativistic conformal theories, not of non-relativistic conformal theories, so that puzzles me.

If Milgroms comment about this emerging scaling symmetry is true, I'd expect that its emergence for a << a_0 translates itself into an Inönü-Wigner contraction and/or extension of the Bargmann algebra to some new symmetry algebra which contains this z = 1 scaling symmetry (just like the non-relativistic limit translates itself to a similar extension+contraction of the Poincaré algebra). It's gauging should then reproduce the Newton-Cartan variant of Milgrom's MOND.

Anyway, that's why this scaling symmetry caught my attention in the first place. It would be nice to also understand it from Khoury's point of view, hence my question.