Which are the good introductory books on modern mathematical physics? Which are the more advanced ones?
I already read Whittaker's Analytical Dynamics, and I am reading Arnold's Mathematical Methods of Classical Mechanics. However, I am not so much interested in books about classical mechanics, neither am I interested in books for engineers. I have seen the related questions but their answers either offer books on classical mechanics, books for engineers, books for the public, or books on introductory mathematics, neither of which is any of what I need. I am already aware of Spivak's and of Landau’s books, so no need to include those. I appreciate rigor and I am not interested in popular books. For instance A Road to Reality is not appropriate but Lectures on Quantum Mechanics for Mathematics Students is.
I am asking in particular about books on quantum theories and on cosmology. I did not put it in the title, because I want to include unfalsifiable theories. I mean anything from string theory thorough conformal cyclic cosmology to loop quantum gravity.
To state my background I am in the senior year of an undergraduate mathematics program. I took courses in classical mechanics, continuum mechanics, and mathematical models of physics. The last one concluded with an application of quantum mechanics in soliton theory. I audited a course in quantum field theory and a course in the calculation of conformal Feynman amplitudes. This course assumed knowledge in conformal field theories, which I lack.
I have taken or at least partially audited most of the offered courses in pure mathematics. If someone asks in a comment, I will make those explicit. I have at best poor knowledge of group theory, representation theory, Lie groups, operator algebras, symplectic geometry, analysis on manifolds, complex manifolds, differential topology, or algebraic number theory. I plan to cover some of those in part during the summer semester and in a master program.
So what are good books for a young mathematician who wants to dabble in physics?