# A "UV completion of a theory of Superfluid Dark Matter"

1. Jan 15, 2018

### mitchell porter

http://arxiv.org/abs/1801.04083
UV completion of a theory of Superfluid Dark Matter
Andrea Addazi, Antonino Marciano
(Submitted on 12 Jan 2018)
We show that a model of superfluid dark matter, modifying the Newtonian potential and explaining galactic rotational curves, can be unitarized by the formation of classical configuration in scattering amplitudes. The classicalization mechanism may also trigger the formation of the superfluid state from the early to the late Universe.

Khoury and Berezhiani's theory of a MOND superfluid is one of the most interesting theories of dark matter, but it's only an effective theory. This paper proposes that the theory is completed by the "classicalization" mechanism of Dvali et al, according to which there are large classical configurations, akin to black holes, which show up at high energies.

Dvali et al originally proposed classicalization in 2010 as an alternative to the existence of a Higgs boson. At the time Lubos Motl argued that the concept is flawed and that black holes are the only objects with the desired property. So one thing I would like to know, is whether virtual black holes could provide the UV completion to a MOND superfluid?

2. Jan 15, 2018

### Urs Schreiber

While I don't know the answer to your exact question, I notice that "superfluid dark matter" is just one term of a class of very similar ideas going back all the way to Baldeschi-Gelmini-Ruffini 83, which are alternatively known as "Bose-Einstein condensate dark matter" (Sin 92) or "fuzzy dark matter" (Wu-Barkana-Gruzinov 00) and often identified with ultralight axion dark matter models (e.g. Erken-Sikivie-Tam-Yang 12).

Edward Witten recently pointed out that a natural conceptual origin of these ultralight axion dark matter fields is, of course, string theory (Hui-Ostriker-Tremaine-Witten 17), where the axion field is generic (here).

So if you'd ask for UV-completions of these BEC/superfluid/fuzzy dark matter models, what immediately comes to mind is string theory.

Last edited: Jan 15, 2018
3. Jan 15, 2018

### MathematicalPhysicist

Obviously, if string theory is the theory of everything then everything should appear there... :->

4. Jan 15, 2018

### Urs Schreiber

To turn this around to something that, i think, deserves thought:

While stabilization of modui fields in string theory (hence their disappearance from the observable spectrum) has received lots of attention, it seems that the generic prediction of axion fields in string theory tends to be relegated to side remarks. But taking this seriously, the presence of axionic dark matter ought to be a generic stringy signature.

I am not expert enough on the subtle details, I hope people will sort this out cleanly.

5. Jan 25, 2018

### mitchell porter

I feel like a good start has been made on understanding axion dark matter in string theory, in the several dozen papers on the "stringy axiverse". You get roughly 5 to 100 species of axion, depending on the number of moduli, and their masses can fall anywhere across an enormous range of values, again depending on the specific vacuum. (I would be interested to understand the situation in nongeometric vacua.)

It's good to make progress in understanding what string theory can predict, and some of those vacua may give a viable form of fuzzy DM. However, with respect to MOND... Fuzzy DM is not inherently MONDian. Fuzzy DM does improve on cold DM in certain qualitative respects. But MOND makes a successful prediction that neither CDM nor FDM makes.

MOND explains the orbital velocities of outlying stars by proposing a deviation from Newton's law. Since in MOND's simplest form (no DM), the baryonic matter of a galaxy is the only gravitational source, MOND predicts that the asymptotic orbital velocity of stars in a galaxy depends directly on its total baryonic mass. This is what is observed (baryonic Tully-Fisher relation).

On the other hand, while a shell of invisible dark matter stretching far beyond the stars is capable of changing the rotation profile of a galaxy, the orbital velocity of the outermost stars will depend on the visible mass plus the mass of the dark matter halo. There's no reason for the Tully-Fisher relation to track the baryonic mass as tightly as it does.

The dark matter theories of Khoury and Berezhiani do provide a reason, because their DM superfluid is constructed specifically to mimic the MONDian modification of Newtonian dynamics, including its tight dependence on the baryonic mass. In one version (arXiv:1507.01019), the phonons of their superfluid interact with baryonic matter, and that is the MOND force. This is what Addazi and Marciano are working with.

The other version (arXiv:1602.05961)... it hasn't clicked for me yet, how it works. It's as if it's closer to the usual DM scenario, but with the DM halo having a special MOND-friendly profile. But I know I'm missing something.

A MOND superfluid is something special, it's not just an "ordinary" DM superfluid, it's a DM superfluid that can reproduce the baryonic Tully-Fisher relation. And it's not clear to me whether stringy axions can create a MOND superfluid. In the 2015 theory of Khoury and Berezhiani, the superfluid has a very specific equation of state, an unusual one but one that does exist e.g. in some cold atomic systems. The 2016 theory of Khoury offers more latitude with respect to equation of state, but I don't really understand how it works so I can't judge its compatibility with the axiverse.

P.S. Regarding the paper that started this thread, I noticed that the UV cutoff is at 1 meV! So no, I don't think the UV completion will involve black holes.

6. Jan 26, 2018

### Urs Schreiber

Thanks for looking into details.

There were claims early on that the observed almost-flat galactic rotation curves do follow from the basic assumption of dark matter behaving wave-like on galactic scales. It seems that this goes back to
• Sang-Jin Sin,
"Late time Cosmological Phase Transition and Galactic Halo as Bose-liquid",
Phys. Rev. D50:3650-3654, 1994
(hep-ph/9205208)
In the recent review
it has a bunch of pointers in this regard on p. 3: "There are many works explaining the rotation curves of dwarf [17, 23, 69], and large galaxies [29, 43, 70–78] in this model."

I haven't looked into this in more detail, though. If you think these claims are wrong, I'd be interested in hearing your account.

7. Jan 29, 2018

### mitchell porter

See arXiv:1107.2934. The baryonic Tully-Fisher relation is an empirical relation between the baryonic mass of a galaxy and the asymptotic rotation velocity. The baryonic mass is proportional to a power of the velocity. CDM predicts that to a first approximation, this is a cubic relation (section 3.1), but the exponent can be nudged away from 3 by astrophysical processes. MOND straightforwardly predicts that it is a quartic relation (section 3.2). The data indicate a quartic relation. So CDM models can be massaged to give an exponent like 3.9, whereas MOND simply gives 4.

Fuzzy DM (etc) does not generically change this property of CDM. Fuzzy DM changes other aspects of CDM, like getting rid of cusps in the density profile. The Khoury-Berezhiani DM is designed to reproduce the MOND force law, and this is new. (See e.g. JiJi Fan's 2016 study of how to obtain ultralight scalars in particle physics, where she remarks on the novelty of their proposal, and the distinctive form of the scalar potential they employ.)

8. Jan 29, 2018

### Urs Schreiber

Thanks for the pointer. That's a nice article.

I am not exactly sure anymore what we are debating. There is 1) the curious astrophysical observations one aspect of several of which is Tully-Fisher, then 2) by-hand fits of this data by postulating new laws of physics or new interactions chosen by hand with the sole purpose to fit this one type of observation on a small range of scales and then 3) there are general theories of physics, internally consistent and consistent all other physics, which exhibit the possibiliy to have effective corners in their moduli spaces which makes them look like 2) and hence reproduce 1).

It is clear that by playing with 2) unconstrained by 3) then one gets more easily more exact fits to 1), while if one is more careful to stay in a consistent framework 3) then it is more work. Progress here is slower, but more sustainable.

I suspect this is uncontroversial. But I am guessing now that you are really after the question of UV-completions of "theories" as in item 2). I am not sure if this is a sensible question, though. Before "UV-completing" these "theories" the issue is to embed them into actual theories in the first place, as in 3). Otherwise it seems an game with too few constraints to be interesting.

But maybe I am missing the point that you are arguing. All I really had to point out in #2 is Witten's argument that the general kind of ingredient that is needed for many of the games in 2) is naturally provided in 3) by string theory. Of course this is not a proof of anything, just a plausibility argument.

9. Jan 31, 2018

### mitchell porter

We differ in our estimation of the importance of MOND. Compared to CDM, MOND is the superior theory at galactic scales. Despite the title, I started this thread because the paper is about MOND, not because it is about superfluid DM. If superfluids couldn't give us MOND, I would be looking for some other macroscopic quantum explanation.

I am suspicious of the flexibility of the auxiliary astrophysical hypotheses which allow CDM models to approximate a value of 4 for the exponent in the baryonic Tully-Fisher relation, when that is the value that comes directly from MOND. It's like how asymptotic safety predicted the Higgs boson mass with great precision, suggesting that something has tuned the standard model to the edge of metastability, and yet the modeling focus is still on tweaking low-energy supersymmetry to match the observed mass approximately. (Maybe we should be looking for an asymptotically safe UV completion of MOND!)

Maybe the axiverse can give us MOND. Maybe the axiverse can give us CDM at supragalactic scales, and something from the extended gravitational sector gives us galactic MOND. And yes, maybe MOND (and the critical Higgs) are just wrong, and in both cases it's an illusory simplicity emergent from complexity. But for now, I prioritize the simpler explanation.

10. Feb 10, 2018

### Urs Schreiber

Generally, thanks for your thoughtful replies!

I believe that I fully appreciate the importance of MOND. The difference is, I think, whether to regard it as a theory.

It seems obvious to me that MOND is a parameter fit. That this fit works so exceedingly well in its (small) range of applicability is, to my mind, the precise statement of a question rather than the statement of an answer.

That question needs an answer. But it needs an answer that does not throw out all of established physics just to fit some astrophysical observations in a comparatively small range of scale. We need to find a coherent answer, that fits into the established framework of modern physics.

That's why I am cautious about the lure of introducing and then tuning by hand a coupling here and a something there, just because that gives a good fit to MOND, which is itself just a fit to data.

But that's okay, we can agree to have a different attitude toward this (if we really do).

11. Feb 10, 2018

### Urs Schreiber

It seems to me that this is is not the full statement of Arvanitaki,Dimopoulos,Dubovsky,Kaloper,March-Russell 09, if that's what you are referring to. While they do find that masses of stringy axioms are distributed over a large range, they find that the distribution (i.e. probability density) of masses across this range is uniform on lograrithmic scale.

This means that the majority the stringy axion field species has tiny positive masses, while only very few have larger masses and only a tiny number of them has really large masses.

There is a useful summary that Acharya-Kane-Kumar 12 give on their p. 3 (my emphasis added):

"Now consider the axions. Due to the shift symmetries mentioned above, there are no perturbative contributions to their potential. Non-perturbative effects though, such as strong gauge dynamics, gauge instantons, gaugino condensation and stringy instantons will generate a potential for the axions. Because any such contribution is exponentially suppressed by couplings and/or extra-dimensional volumes, in our world with perturbative gauge couplings (at high scales), the axion masses will be exponentially small.

"Furthermore, since there are large numbers of axions in general, their masses will essentially be uniformly distributed on a logarithmic scale [5]. See [6] for a detailed calculation of axion masses in string/M effective theories.

"Like the moduli, the axions are also very weakly coupled to matter and therefore do not thermalize in general. Moreover, since their masses are tiny - ranging from $m_{3/2}$ to even below the Hubble scale today - many of them, including the QCD axion, start coherent oscillations during the time that the moduli are dominating the energy density, but before BBN."