SciPost Submission Page
Dark Matter Superfluidity
by Justin Khoury
Submission summary
As Contributors:  Justin Khoury 
Arxiv Link:  https://arxiv.org/abs/2109.10928v1 (pdf) 
Date submitted:  20210929 14:47 
Submitted by:  Khoury, Justin 
Submitted to:  SciPost Physics Lecture Notes 
Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
In these lectures I describe a theory of dark matter superfluidity developed in the last few years. The dark matter particles are axionlike, with masses of order eV. They BoseEinstein condense into a superfluid phase in the central regions of galaxy halos. The superfluid phonon excitations in turn couple to baryons and mediate a longrange force (beyond Newtonian gravity). For a suitable choice of the superfluid equation of state, this force reproduces the various galactic scaling relations embodied in Milgrom's law. Thus the dark matter and modified gravity phenomena represent different phases of a single underlying substance, unified through the rich and wellstudied physics of superfluidity.
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Anonymous Report 1 on 20211019 (Invited Report)
Report
In these lectures, the author introduces and motivates the hybrid DMMOND model superfluid dark matter. I find them to be clear and wellwritten, providing a good basis to understand superfluid dark matter.
I have a few comments and suggestions:
1. On p. 2, references [2, 3] are not really about the MDAR, as suggested in the text, but about the RAR. Of course the RAR and the MDAR are equivalent, but giving only these references might confuse readers who don't already know this.
2. On p.3, below (4), the author writes that there is a solution $a_\phi = \sqrt{a_b a_0}$. This is usually a good approximation but is strictly true only in spherical symmetry and other special cases. It might be good to note this to avoid confusion for readers who try to rederive this result.
3. On p. 4, I think the exponent in (6) is missing an overall minus sign. Similarly, I think the righthand side of (8) on p. 5 is missing an overall minus sign.
4. On p. 8, $\psi_0$ is introduced as the condensate wavefunction. I know it is not uncommon to refer to $\psi$ as a wavefunction, but I find this causes a lot of confusion for students since $\psi$ is not actually a wave function, $\psi^2$ is not a probability density. Conceptually, $\psi$ is much closer to the quantum/classical electromagnetic field (or its fourpotential) than to a QM wavefunction. It would be good to change the naming or briefly explain this to avoid confusion.
5. On p. 14, the author derives the phonon force and the density profile from the Lagrangian (58). But opposite limits are used for the phonon force and the density profile. For the phonon force to look like $\sqrt{a_0 a_b}$ (eq. (61)), the gradient terms (with $\vec{\nabla} \theta$ or $\vec{\nabla} \pi$) in the Lagrangian must dominate the chemical potential terms (with $\mu$). For the density profile to have, e.g., the equation of state claimed in (63) / (64) the opposite limit is needed. Maybe the density profile (but not the phonon force) is supposed to be for the case without any baryons? In this case it should probably be pointed out that the derived density profile does not directly apply to galaxies. In any case, the two opposite assumptions about which terms dominate should be made explicit to avoid confusion.
6. On p. 15, the author writes that it is not surprising that the density profile is cored. I'm not quite sure what this refers to. Is it that LaneEmden equations generally give cored profiles? A clarification would be helpful.
Anonymous Report 2 on 20211018 (Invited Report)
Strengths
1. This article gives an introduction to one of the most interesting dark matter models to have been introduced in recent years.
2. It is at a level more accessible to students than anything that can be found in the existing literature.
Weaknesses
This is not really a weakness, only a modest wish from someone who will give this reference to some of his students, based on their typical background in his corner of the world:
1. BoseEinstein condensation, which most students will have been introduced to in a course on statistical physics, is presented in quite some detail. In contrast, some knowledge of effective field theory, which students with only a basic course in quantum field theory will not have been exposed to, is more or less taken for granted.
Report
The acceptance criteria are clearly met: The article provides a correct, very systematic and intelligible presentation of a topic of ongoing interest. It will be a very valuable reference for students (and their thesis advisors).
It may be an oversight of my part, but I cannot see that [68][70] in the reference list are referred to in the text. It would perhaps be natural to say something about vortices after concluding in section 6 that the flow is irrotational, and in that case these references would be relevant.
Requested changes
1. Add a reference to an introductory text on effective field theory at the start of section 4.