What Math and Physics Background Is Required to Study Cosmology?

[bobsmith76]

What do I need to know before I can study Cosmology. I think I'm going to read this text:

https://www.amazon.com/dp/0198526822/?tag=pfamazon01-20

Cosmology by Steven Weinberg. I'm going to read this College Physics text first by Serway

https://www.amazon.com/dp/0840062060/?tag=pfamazon01-20

And I will have a good grasp of calculus soon. What other math and physics do I need to know?

Also what math does Cosmology employ most?

 

[mal4mac]

What do I need to know before I can study Cosmology. I think I'm going to read this text:

https://www.amazon.com/dp/0198526822/?tag=pfamazon01-20

Cosmology by Steven Weinberg. I'm going to read this College Physics text first by Serway

https://www.amazon.com/dp/0840062060/?tag=pfamazon01-20

And I will have a good grasp of calculus soon. What other math and physics do I need to know?

Also what math does Cosmology employ most?

I sweated over Weinberg's other book on this subject for my MSc project in Astronomy - that's "Gravitation and Cosmology". That's an essential prerequisite. But there are many others! If you look at the first chapter of "Cosmology" in "Look inside" you see that to understand the derivation of equation 1.1.3 you need to understand G & C up to section 13.2.

G & C itself requires a lot of background, or at least a lot of "mathematical maturity". For instance, look at the second equation in G&C - it shows the distance between two points in a non-Euclidean geometry, with *no* hand-holding. So if you haven't encountered that kind of geometry before you need to either (i) accept it and move quietly on or (ii) dig into Weinberg's references... and buy another book... which no doubt is equally high level... and requires another book... and another book...

I remember haunting the university library and looking through dozens of books in desperate search of some "hand holding", and mathematical background for just about every page of Weinberg. It's that tough. Tougher than anything, except the book you're aiming to read...

 

[Vanadium 50]

If you read the Amazon description of Weinberg's text, it says "it divides into two parts, each of which provides enough material for a one-semester graduate course."

If you read the preface of Serway's text (from the link you provided), it says "College Physics is written for a one-year course in introductory physics usually taken by students majoring in biology, the health professions, and other disciplines including environment, Earth and social sciences, and technical fields such as architecture. The mathematical techniques in this book...do not include calculus."

So there's about 15 college courses separating those two books.

 

[bapowell]

Weinberg's book is probably too advanced for beginning reading, being more appropriate to graduate-level study.

You can begin to develop an understanding of the concepts and mathematics of cosmology without it, but eventually you're going to need to study general relativity. It is based on the mathematics differential geometry.

 

[twofish-quant]

I like Dodelson's "Modern Cosmology". It something that a junior physics major can understand, and once you've finished Dodelson then Weinberg is going to make a lot more sense.

One other thing is that it would be helpful if you created a personal wiki page or a blog on the topic. There's a lot of "hand-holding" material on the internet that can get you from point A to point B, and someone needs to organize it, and it could be you.

Something that I wish would exist is some sort of hypertext version of advanced physics texts, so that you start with Weinberg, and when you start with something that you are clueless about (which will start on page 2), you click on it, and it eventually it gets you to something that newbies can deal with.

 

[twofish-quant]

I remember haunting the university library and looking through dozens of books in desperate search of some "hand holding", and mathematical background for just about every page of Weinberg. It's that tough. Tougher than anything, except the book you're aiming to read...

I had the same experience. At the time (and this was in 1989 and involved one of Weinberg's earlier books), I wished someone would invent something where you could read the text of a book, and if there was something that you didn't understand, you could click on the text and some page in some other book would come up and explain to you what you didn't understand, and if you didn't understand that, you'd keep clicking until you found something that makes sense.

Anyone hear of any sort of invention like that?

More seriously, the "click one piece of text to get to some other text" problem has been solved. The thing that no one has done (and Wikipedia has gotten closer than anyone else) is to actually work out the links themselves. The frustrating thing is that there is no technological barrier. The barriers are legal and administrative.

We haven't got there yet, but we are really, really, really close.

 

[twofish-quant]

Also modern cosmology involves a ton of statistics.

 

[yenchin]

Liddle's "An Introduction to Modern Cosmology" is quite readable (and short) as an introductory text. You might also want to complement it with a semi-popular science book [more like a textbook actually] that I really like (some explanations are really good), try Duncan and Tyler "Your Cosmic Context"

 

[cepheid]

I had the same experience. At the time (and this was in 1989 and involved one of Weinberg's earlier books), I wished someone would invent something where you could read the text of a book, and if there was something that you didn't understand, you could click on the text and some page in some other book would come up and explain to you what you didn't understand, and if you didn't understand that, you'd keep clicking until you found something that makes sense.

Anyone hear of any sort of invention like that?

No, but it would be seriously cool. Every author tries to keep re-inventing the wheel, thinking that their text will be the best and most self-contained to date (at least for the audience and purpose they are targeting). It would be so much better if instead we could pool together related knowledge from a bunch of different sources, allowing one to build on one's knowledge incrementally without having to search endlessly to find out which book has the background you need to understand the current one that you're supposed to be reading. I think it's a neat concept.

I like aspects of Dodelson as well, although it has its drawbacks. For a treatment that is even simpler still, I find that the chapters on cosmology from Galaxy Formation by Malcolm S. Longair to be pretty helpful. It's sort of at the level of "cosmology for observational astronomers." He spends one chapter giving a fairly perfunctory overview of GR, and then introduces the Friedmann equations in the next chapter. He states that they can be derived from the Einstein field equations for the case of an isotropic and homogeneous world model, but does not bother to do so himself. To the OP: for now, if you accept the Friedmann equations as a given, and if you are fairly well-versed in differential equations and calculus, then I think that this might be a good place to start, and you can get pretty far in understanding the properties of the world models and what they predict, as well as a good review of observational cosmology.

 

[twofish-quant]

No, but it would be seriously cool. Every author tries to keep re-inventing the wheel, thinking that their text will be the best and most self-contained to date (at least for the audience and purpose they are targeting).

One thing that people should be thinking about is how do textbooks work in the age of the internet. Wikipedia, for all of it's problems, is the closest thing that I've seen into seriously new thinking about how to set up a textbook.

It's not so much the authors, as the publishers. The reason that books are self-contained is that it fits well with copyright law. If you have a "diffused textbook", it's not clear who gets paid what and how. I'm sure someone is going to work it out.

It would be so much better if instead we could pool together related knowledge from a bunch of different sources, allowing one to build on one's knowledge incrementally without having to search endlessly to find out which book has the background you need to understand the current one that you're supposed to be reading. I think it's a neat concept.

The problem is that no one (yet) has figured out how to do this. If you have one person do it, then they are going to have to eat somehow, so you need a payment mechanism. You can try to crowdsource this, but then you have to figure out how to split up the tasks, and you have to figure out how to create an environment in which things "self-organize."

He spends one chapter giving a fairly perfunctory overview of GR, and then introduces the Friedmann equations in the next chapter. He states that they can be derived from the Einstein field equations for the case of an isotropic and homogeneous world model, but does not bother to do so himself.

That's one piece of advice that I'd give someone that wants a quick start to cosmology. Don't go too deep into General Relativity. Get a "hand waving" explanation for the Friedmann equations, once you have that then you can learn the physics concepts, and once you have that, then you can go back to the Friedmann equations, and look at the GR issues in more depth (or not).

If you want to get super-hand-wavy you can do cosmology is a Newtonian framework and then talk about how GR is different. This is useful pedagologically because a lot of the important features of cosmology are gravity model independent.

That's what the professionals do. Someone works out the basic equations and then this gives a framework that people can use to do calculations is a more or less Newtonian setting. Now whether to what extent that's a valid way of doing things is a topic you can spend a few years writing your doctoral dissertation on (it's called the backreaction problem). The thing is that it's a hard problem and even smart people can deal with only one hard problem at a time, so one tactic is to massively simplify the GR model so that you can go deep looking at something else. Dark matter or galaxy evolution for example.

One problem with going straight to Weinberg is that it's designed for graduate researchers who are going to be writing dissertations on the stuff. Once you get through Weinberg, then you'll be ready to start on your dissertation and start writing papers on cosmology.

 

[mal4mac]

I like Dodelson's "Modern Cosmology". It something that a junior physics major can understand, and once you've finished Dodelson then Weinberg is going to make a lot more sense.

That's a bit tough as well - note equation 1.9 where knowledge of Fourier transforms and the Dirac delta function are assumed. For someone at the level of Serway I'd recommend:

Cosmology by Michael Rowan Robinson

Rowan Robinson has been a big name in observational cosmology in the UK since the seventies. I remember using the first edition in a second year undergraduate course many moons ago. I really enjoyed it - especially as I thought it was going to be a tough course, but it turned out to be easier than most courses I took. The biggest problem - it might make you complacent. The step from RR to Weinberg is a big one! The difference between beating your head against a pillow and beating it against a concrete wall :)

The fourth edition is quite expensive. I picked up the third edition (1996) cheap and that should be good enough... it includes discussions of inflation and GUT.

I've glanced at the following, "the new kid on the block (in the UK)", which also looks good at this level:

An Introduction to Modern Cosmology, 2nd Edition by Andrew Liddle

Both of these books recommend Weinberg (1972) for advanced study, so you are not going wrong with Weinberg, it's just it should be part of a five year plan! Liddle and RR can be used *now* to keep you interested...

 

[mal4mac]

That's one piece of advice that I'd give someone that wants a quick start to cosmology. Don't go too deep into General Relativity. Get a "hand waving" explanation for the Friedmann equations, once you have that then you can learn the physics concepts, and once you have that, then you can go back to the Friedmann equations, and look at the GR issues in more depth (or not).

If you want to get super-hand-wavy you can do cosmology is a Newtonian framework and then talk about how GR is different. This is useful pedagologically because a lot of the important features of cosmology are gravity model independent.

Yes, this is very good advice - Rowan Robinson takes exactly that approach. GR yields exactly the same cosmological models as Newtonian theory - so you can calculate really neat things using first year physics and say "GR gives just the same results!"

 

[DagmPhys]

I recommend you to watch Susskind's GR and Cosmology lectures from youtube before going into any trouble reading all these books. Enjoy!

 

[mal4mac]

... chapters on cosmology from Galaxy Formation by Malcolm S. Longair to be pretty helpful. It's sort of at the level of "cosmology for observational astronomers." He spends one chapter giving a fairly perfunctory overview of GR, and then introduces the Friedmann equations in the next chapter...

Sounds just like Rowan Robinson's approach - although he doesn't mention Friedmann. If that bothers you, you can add some historical reading. Some popular books can be quite good on the history - I'd recommend Big Bang by Simon Singh.

Attribution & parallel development seems to be a big thing in the history of early 20th century cosmology! This can lead to excess attributions that just get silly - look up "Friedmann–Lemaître–Robertson–Walker metric" in Wikipedia: "Depending on geographical or historical preferences, a subset of the four scientists — Alexander Friedmann, Georges Lemaître, Howard Percy Robertson and Arthur Geoffrey Walker — may be named (e.g., Friedmann–Robertson–Walker (FRW) or Robertson–Walker (RW) or Friedmann–Lemaître (FL))".

Rowan Robinson neatly cuts this to *one* option "Robertson–Walker metric", without mentioning the other permutations at all. In fact, if at all possible, he reduces the name to one. I guess that's why Lemaître gets mentioned but not Friedmann!

I like RR's "historical figures extra-lite" approach just as much as his "math extra-lite" approach !

 

[bobsmith76]

all around great advice. I guess I'll start with RR and just stick with the hand waving explanations for GR.

 

[Vanadium 50]

I just took a look at Rowan-Robinson's book, and I looked at some of your other posts. I think you don't have the mathematical background yet for that, and you might need to work on your algebra first.

 

[twofish-quant]

Yes, this is very good advice - Rowan Robinson takes exactly that approach. GR yields exactly the same cosmological models as Newtonian theory - so you can calculate really neat things using first year physics and say "GR gives just the same results!"

Except that it doesn't :-) :-)

However, it's a useful approach from a teaching perspective. You start Newtonian. Then you bring in GR, and then you show how GR gives different results from Newtonian and why, and *then* you start talking about Riemannian manifolds and Ricci tensors.

One reason that it works, is that if you just start with GR, you miss the "essential point" of cosmology which is that when you calculate the entire universe, the math in fact becomes much more simple because of symmetry.

One analogy for what is going on is that you are trying to get to the top of Everest, and there are several ways of doing getting there. And in some of the places, it's easier now because someone has put a ladder to get over the difficult parts.

 

[cristycs]

prerequisites for cosmology: Passion