General feedback on milestone I
Figures:
You have generally done a good job here. The figures are nice.
Theory and implementation:
Again generally good. Make sure all relevant things are included. E.g. if you want to talk about 1sigma constraints you should add some details about how these are computed.
Demonstrating your code is correct:
Some of you have done a good job on this, while some of you have very little. If it is possible to do a simple analytical estimate for what quantity X (e.g. in the radiation dominated regime you can show that Hp ~ 1/a and eta ~ a so we should have Hp’/Hp = 1 and eta Hp/c = 1 in this regime) should be then this is a nice and simple thing to include in the plots or simply mention it when you discuss the results. This will not always be possible, but the few places you can easily do this then this is a good idea.
MCMC fitting:
What discussing these results try to think about what it tells us about our Universe: what does the data tell us about OmegaLambda (is OmegaLambda = 0, i.e. no DE, possible?), what does the data tell us about OmegaK (is the universe flat or not? Is the data sensitive to this)? What is the value of H0 compared to our fiducial cosmology? Is the best-fit you get a “good” fit? Whenever we do a fitting we will always find a “best-fit”, but if the fit is “good” is another question. Compare the results to our fiducial cosmology (which comes from fits to the CMB and large scale structure data, i.e. data on large scales). Does the values agree? For H0 you might want to read a bit about the “Hubble Tension” (https://arxiv.org/abs/2103.01183) - a current problem we are facing in cosmology where different probes gives conflicting values for the parameters. This is a sign that LCDM might not be the correct model and needs to be modified (maybe some missing physics) or it might be due to observational systematics. Nobody knows yet.
General point on interpreting your results:
If you get results you don’t expect then *don’t* try to confidently “explain” this away unless you believe in it. Some of you have tried to blame results on approximations when there are none. Is so then you should have checked if this could be the case. Some of you have tried to explain it away using physical arguments. And some of you have not commented on it at all. The latter is the worst, but when you write a paper you have to stand by what you write. So only write statements you are comfortable with. It’s hundred times better to say “We don’t know the reason for this, but possible explanations are: …” rather than “We see that… This is of course because (add random argument I clearly don’t believe in but added it just to have something to say so it does not look like I don’t understand)”. This is very important when writing up scientific results. Don’t be discouraged from speculating if needed, this is encoiuraged, but make sure it’s clear in the text it is speculation.
Latex tips:
If you want text inside a math-environment (e.g. “x_{min} = 1” or “x =2 if t > 0”) then you can use \text{mytext} or {\rm mytext} or \mathrm{mytext} to get a normal font.
All standard mathematical functions are availiable as \sin, \cos, \sinh, \exp and so on.
On the coding:
Even though we are going to use OmegaK = 0 in the rest of this project, your background need to be able to work with general OmegaK to do the fitting. In particular you need to implement the general expression for “r” as function of comoving distance chi and curvature OmegaK.