How important is quantum theory to cosmology/astrophysics?

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I'm asking this to help with making subject choices. One thing I'd like carry away from this degree is an overall understanding of the origin and structure of the universe. I'm wondering how much quantum mechanics and quantum field theory should I take to gain this understanding. I have heard of quantum cosmology but I've no idea how influential/essential it is to the big picture and the level of QM it involves. There's only so much classes I can take so I want to know what's crucial and what's not. BTW, I don't intend work in cosmology or astrophysics, I just want to know it.
 
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It depends on what level of understanding you want, and how advanced you want to get.

At a "beginner" level, you don't need a lot. Get Weinberg's book _The First Three Minutes_ for example. It's an excellent intro, and as accessible as the subject can be made. After you read that book, ask yourself how much more you need.

To go beyond that you need to start thinking about things like nuclear synthesis and branching ratios and cross sections. And then some stat mech, and statistical thermodynamics. And probably some general relativity for good measure.

When you read Weinberg's book _Gravitation and Cosmology_ you may find it tough sledding because he pulls in so many widely spaced topics. You will be reading along about gravity, and suddenly he is bringing in the equation of state of plasma. And so on. Once I attended a conference at which he spoke. And he could do this stuff "on his feet." So if you want to be brilliant, you need to pack as much of this stuff into your head as you can.
 
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Ask your advisor. It may be that QFT is useful to your field.