A. Cross-disciplinary physics
Gravitation is the driving force of the cosmos and so Einstein's General Theory of Relativity is the appropriate tool for modeling the Universe. However, that alone is not enough: other branches of physics have played a key role in building what has emerged as a "Standard Model" for cosmology.
Nucleosynthesis played an early role in defining how the light elements formed (Alpher et al., 1948): the abundances of Helium and Deuterium play a vital part in confronting our models with reality. In following how the cosmic medium cooled sufficiently to enable gravitational collapse to form galaxies and stars we need to understand some exotic molecular chemistry.
Today, our understanding of high energy physics plays a key role: some even defined a new discipline and refer to it as "astro-particle physics". We have strong evidence that there is a substantial amount of dark matter in galaxies and clusters of galaxies. So far we have not been able to say what is the nature of this dark matter. There is also growing evidence that the expansion of the Universe is accelerating: this would require an all-pervading component of matter or energy that effectively has negative pressure. If this were true we would have to resurrect Einstein's cosmological constant, or invoke some more politically correct "fifth force" concept such as quintessence.