Dark Matter in Astrophysics/Cosmology

These lectures notes are supposed to provide introductory material on dark matter in astrophysics and cosmology.
The author manages to cover a number of points, including evidence for dark matter, distribution, and constraints.

Including all this material was not a good strategy though, since in my opinion quantity came at the expense of quality. My major criticism is the following:
- these notes contain a very comprehensive list of facts, but no explanations. As such, the paper can provide a good summary for someone who already knows the topic, but it would not be helpful for someone who is starting to learn it (like a student). Thus, I would not identify the paper as lecture notes, rather as a review (to be anyhow improved). For this reason, I do not think that the paper can be accepted in the journal SciPost Lecture Notes or, at least, it would require a very dramatic improvement of the text.

Regardless of my decision, and of whether the paper will be published here or in another journal, I would like to provide the author some inputs on minor points to be improved:
- The current version of these lectures notes appears to be way too colloquial, and there are many typos. Also, the author uses contracted forms (it's, won't, 'll, 've) that should not be used in proper written English and should be replaced by their full form (it is, will not, will, have). There are also inconsistencies in the notation (use of $\epsilon$ versus $\rho$).
- I would suggest that the author, after eq. (1), spells out the word "dot" instead of using the math symbol $\dot$, which in the text appears invisible.
- After "Universe is very close to flat" k should not be k=0, but rather $k\approx 0$.
- The author says that they will use natural units, but then re-introduces the speed of light $c\neq 1$ in eq. (4). This makes the explanations confusing.
- An explanation of redshift is missing. More generally, a lot of concepts are introduced without explanation.
- A derivation /explanation of eq. (6) is missing. Same for eq. (14).
- Right after eq. (19), it would be really good if the itemized could be accompanied by a figure showing the various regimes.
- At the beginning of section 1.4: technically, in the context of GR it is wrong to speak about "force of gravity". Right after that, "a scale" is introduced, but it is not clear what the author is referring to.
- A definition of Jeans length is missing.
- Close to eq. (23), it would be nice to have an explanation of how the pivot scale is chosen.
- The explanation in the subsection on "Modified gravity" seems to be a bit too short, considering how much literature is around. I also think that, from that paragraph, a student could erroneously think that dark matter provides better explanations than modified gravity, while this is not necessarily the case.
- "Lab" is too colloquial, I would use the extended word.
- Footnote 8: not a very useful comment, it would be more useful to have an explanation of what the 6 words mean.

1- very clearly written and pedagogical introduction to dark matter
2- many references for further reading
3- accessible with no prior knowledge of the subject
4-both historical and modern developments covered

This is an excellent introduction to the topic of of dark matter, well suited for students with little or know prior knowledge of the subject, but also for researchers looking for key references on specific topics.

My comments are only very minor corrections:

- in Eq (1), Newton's constant isn't introduced
- a few times \rho appears instead of \epsilon, eg below Eq (2), in the caption and label of Fig 1, in Section 1.4, ...

1 - This set of lecture note is well written
2 - It provide a pedagogical explanation of relevant topics

This is a set of lecture notes for an introductory course on Dark Matter and Cosmology. The material covers the basic elements of Cosmology and provides a direct road to further topics involving Dark Matter.

This review is part of a series of lecture notes on Dark Matter and I believe it accomplishes the goal of being accessible for students while working as a background source for the other lecture notes.

As a minor comment, I would suggest to the author to do a quick check on the notation for the energy density in different parts of the manuscript. In some points, the energy density is denoted by $\epsilon$, while in others it is denoted by $\rho$. It would be better to have a uniform notation.

In general, I believe the paper is compatible with the standards of this journal and I recommend it for publication.