Dark Matter in Astrophysics/Cosmology

I'm grateful to Referees 1 and 2 for their positive comments ("well written, very clearly written, pedagogical, accessible, excellent introduction") on the lectures notes.

Referee 3 clearly dislikes the scope and style of the lecture notes, however different people can legitimately make different decisions about how to present material. The referee may have been taught that contractions shouldn't be used in written English, however this view isn't universally shared. In writing these notes I've prioritised readability over "proper[LY] written English".

As Sec. 0 explains, the lectures on which these notes are based were designed to "provide the participants in the ‘Les Houches Summer School 2021: Dark Matter’ with the background knowledge of cosmology/astrophysics required for the other courses during the School". As explained in the notes, it would usually take 20+ hours of lectures to cover the material in 'Sec. 1 Introduction to Cosmology' and "therefore our treatment will be necessarily superficial (and unsatisfactory for fans of rigour)" and "This will be a rapid ‘crash course’ for people who haven’t already studied such material and a recap for those who have.". The positive feedback from the participants in the School indicates that they found this approach effective.

In response to Referee 1 and 2's specific comments I have:

i) changed the errant rhos (for energy density) to epsilons (in the text after Eq.(2), in Fig. 1 and its caption, in the 2nd paragraph of Sec. 1.4) and where it's the mass (rather than energy) density that's being referred to I've now explicitly stated this.

ii) Inserted the definition of G after Eq.(1).

Here are my responses to Referee 3's specific comments:

-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.

Done.

-After "Universe is very close to flat" k should not be k=0, but rather k≈0.

Done.

-The author says that they will use natural units, but then re-introduces the speed of light c≠1 in eq. (4). This makes the explanations confusing.

I have removed the one errant factor of c.

- An explanation of redshift is missing. More generally, a lot of concepts are introduced without explanation.

Redshift is explained ("The expansion of the universe leads to cosmological redshift of the wavelength of photons: lambda proportional to a”.). The omission of a full derivation is deliberate: the benefits of doing it in the lectures wouldn’t have justified the time taken.

- A derivation /explanation of eq. (6) is missing. Same for eq. (14).

I have expanded the explanation of the horizon distance in eq.(6), however this is one of the "incidental, things which I mention briefly, so that if you encounter them you know roughly what they are.”

Eq.(14) is simply, as stated, the ratio of two Maxwell-Boltzmann distributions, with m_{n} ~ m_p. I have added an intermediate step.

-Right after eq. (19), it would be really good if the itemized could be accompanied by a figure showing the various regimes.

Figure added.

-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.

I have removed “force of”. These generic statements apply to any scale. I have added “on a given scale” to the sentence “Perturbations…”

-A definition of Jeans length is missing.

The Jeans length is defined: “Perturbations will grow if t_pre > t_dyn which is the case if R is greater than the Jeans length, lambda_J ∼ c_s t_dyn ∼ c_s/(G ρbar)1/2 “

- Close to eq. (23), it would be nice to have an explanation of how the pivot scale is chosen.

I’ve added “(which is usually taken to be roughly in the centre of the range of scales probed by the data)”. A more detailed explanation is unlikely to be of interest or benefit to the target audience of these notes/lectures.

- 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.

This subsection is intentionally short because, as mentioned, there were a separate set of lectures covering this topic by Justin Khoury. I firmly believe that this paragraph, and in particular the statement “Explaining all of the diverse observations… is [] a major challenge” is a well-balanced summary of the current state of play. I suspect that many dark matter researchers either wouldn’t have included this subsection, or would have been explicitly negative about modified gravity.

- "Lab" is too colloquial, I would use the extended word.

“lab based” is commonly used and understood terminology in the field of direct detection, however I’ve changed lab to laboratory.

-Footnote 8: not a very useful comment, it would be more useful to have an explanation of what the 6 words mean.

Footnote 8 is a light-hearted comment, acknowledging how demanding carrying out these cosmological simulations is. As mentioned earlier in the notes, there were a separate set of lectures by Annika Peter covering numerical simulation in detail, therefore it would have been undesirable to cover this point in detail in either the lectures or notes.

Following feedback from a student who read the notes after submission, I have also added a few words of explanation before the expression for the deceleration parameter today at the top of page 13.

I have also corrected various minor typos.