According to the big bang models, the energy density of the very early universe was extremely high, with the contents of the observable universe compressed into a volume much smaller than that of an atomic nucleus. Under such circumstances, the effects of quantum physics and of general relativity should become equally important, in other words: This era of our cosmic evolution should be described using a theory of quantum gravity. Quantum cosmology encompasses all attempts to apply various candidate theories of quantum gravity to the physics of the early universe, and to describe the universe as a whole as a quantum system.
More information can be found in the spotlight topic Searching for the quantum beginning of the universe. Some quantum cosmological applications of loop quantum gravity can be found in the spotlight texts Avoiding the big bang and Taming infinities with loops.