Book suggestions for WKB approximation and Perturbations in Cosmology

[Genocide]

Hi everyone,
I was wondering if you guys could suggest me some good books in cosmology with finely explained WKB method and Perturbations especially in Structure formation area. I have "The early universe" by Klob and Turner and "Cosmology" by Weinberg , but they seem unpalatable at first look. I am familiar with those methods from quantum mechanics, but application to cosmology seems so confusing.

E-books would be helpful, because we don't really get hard-cover books in my country.

Thanks so much for concern.
Regards,
Genocide

P.S. I am a graduate student by the way.

 

[Jorriss]

I don't know if these are applicable for cosmology in particular but you may want to look into Bender & Orszag.

 

[Genocide]

Yeah , perturbations is in large scale structure formations. Meanwhile I got to check that book. Thanks!

 

[bolbteppa]

Along with https://www.amazon.com/dp/0387989315/?tag=pfamazon01-20 you could use these videos (also here).

I only posted a thread the other day about this book & asked whether anyone would be interested in going through Bender's book over the rest of the summer, posting thoughts, ideas, progress etc... on how they're doing akin to my other thread doing a similar thing so if you're up for doing it I'm game, I've already gone though some of it & am writing up notes but could definitely use the revision as well as reading someone else's take on the material!

 

[Genocide]

Ah that was some dazzling stuff . I think I can somehow understand the Perturbations in Quantum mechanics. But in cosmology , for eg: General theory of Small fluctuations , Chapter 5 , Cosmology by Weinberg, as soon as Ricci Tensor and affine connections come in my way, I just go crazy like hell. The computations turn out to be too much ugly ! Have you done some perturbation stuffs in Tensors , blobteppa ?

 

[George Jones]

Maybe

https://www.amazon.com/dp/052182849X/?tag=pfamazon01-20

but I am not sure how readable this is.

 

[bolbteppa]

Well one interesting thing about perturbations in quantum mechanics is that, according to Bender in the videos, the whole thing is done very dishonestly :tongue: One of the main goals in his book is to set up WKB theory in a way that makes sense, in a way that allows you to become comfortable with dealing with divergent series etc... To give you the freedom to deal with that stuff without qualms.

As for me doing perturbations with tensors, I'm only slowly going through Bender's book & videos on perturbation theory & only almost at the point where I can study divergent series a bit rigorously so no I'm not there yet - though it doesn't surprise me tensor notation would drive things absolutely crazy! If I was in your position I'd always be attributing my lack of being able to work with that stuff as being because I don't know enough about perturbation theory, tensor analysis or just the general literature on the topic thus until I knew all this I'd always have the feeling that this was the reason why (might well not be true, but still). After that I'd guess it was then a research question & feel comfortable that this was a genuine problem to work with & worry about. There are alternatives to perturbation theory that might apply in your case, though if not & you're interested in doing some perturbation theory along the lines of those videos let's go for it & write up our thoughts on the videos + problems etc...

 

[Genocide]

Ahh seems I am slowly getting some ways to deal. Most importantly relaxed mind :) Adomian decomposition method is an interesting method wow..! I admit i didn't know that. But seems they aren't used in standard cosmology literature upto now !