The universe refers to the cosmos; all of space-time and that which exists as part of it. Alternatively, it can refer to the observable universe, which only contains the part we can see. Questions tagged with this should ask about physics at scales the size of the universe or specific properties of the universe
The universe is a subjective term. It generally refers to either (1) all that obeys the known laws of Physics, or (2) all of (1) that is connected to each other by physical geodesics.
The study of the evolution of the universe is a subject of cosmology, which generally uses general-relativity, though, in recent years, there has also been "String cosmology" and "Loop Quantum Cosmology", for instance.