Question

This kind of idea goes back to Baldeschi-Gelmini-Ruffini 83 and due to reinventions it goes by many other names besides "superfluid dark matter" (Berezhiani-Khoury 15), such as "Bose-Einstein-condendate dark matter" (Sin 92) or "fuzzy dark matter" (Wu-Barkana-Gruzinov 00) and several others. The latter term is the one picked up in Edward Witten et. al. 17. A recent review of the literature is in Lee 17.

It's a charming idea:

A model for dark matter made up of massive but extremely light particles, whose de Broglie wavelength is at the scale of galaxies.

The idea is that on scales above that of galaxies, the predictions of fuzzy dark matter agree with the standard cold dark matter models that work exceptionally well on cosmological scales, while on scales of the size of galaxies the quantum properties of these light particles become relevant and change their effect just so as to fix the problems that standard cold dark matter models have on these scales.

A natural candidate for such ultra-light particles are axions. (This is where Witten 17 gets in, since axions are a generic prediction of string theory.)

Comments

It's one of the big observational puzzles of our times that the assumption of WIMP cold dark matter

1.  gives excellent agreement with observation on cosmological scales;
2. has mighty difficulties to match oberservation on galactic scales and below, close to being ruled out on these smaller scales.

The idea of the BEC/superfluid/fuzzy dak matter model is to have the dark matter particle be massive but so extremely light, that just about on the scale of galaxies its quantum effects become non-negligible and serve to fix the second point above, while on larger scales it still behaves like classical WIMP cold dark matter and hence still reproduces point 1 above.

Hence at the moment the assumption that the de Broglie wavelelength of the BEC/superfluid/fuzzy dark matter particle is of the scale of galaxy radii is driven purely by the desire to match observation. If this holds water of course one will want to see if this may be derived from theory, but this seems out of reach at the moment.

Beware that the whole point of these models is to fit observation in the framework of established physical theory, none of this is about wild speculation about the nature of gravity that you mention. On the contrary: The failure of cold dark matter models to work on scales of galaxies and below has given rise to speculation that possibly the very laws of nature need to be modified on these scales ("MOND"), which is problematic,  to say the least. The dark matter postulate is to save established physical theory in view of astronomical observation. But the WIMP model for dark matter, which used to be most popular for years, while working great on cosmological scales, is facing severe problems on smaller scales and is on the verge of being ruled out. The BEC/superfluid/fuzzy dark matter model might be the way to fix it all.

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Right, I hear you voicing these wild speculations, but I try not to react to them too much. :-) That's because wild vague speculation of this sort is not suitable for this research-level forum here! Maybe at Physics.SE they'll show more tolerance. But the topic of BEC/superfluid/fuzzy dark matter is much more fascinating than these wild vague speculations, because it's serious science that actually works.