Black holes and cosmology in quantum gravity

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The term "Quantum gravity" is used to describe any attempt at a theory that applies ideas from quantum mechanics to gravitation. This research area has its origins in the widely accepted view that the physics of small scale objects, such as elementary particles, is described by quantum theory, and that the same should be true for gravity.   Gravitation on large scales, such as the solar system and beyond, is well understood; Newton's theory is a very good approximation to what we see, but has been superseded by Einstein's general relativity. This theory has predicted new effects, such as the bending of light by gravity, that are experimentally verified.  However, Einstein's theory fails  in extreme situations, such as the gravitational collapse of a massive star, or the violent beginning of our universe. In both instances the unknown properties of physics at very small distances become important. At present an incomplete hybrid theory that is only part quantum is available. It predicts that black holes emit radiation, and eventually become smaller than the size of elementary particles. To an extent it also describes the state of our present universe in a way that appears disconnected from its very early quantum gravity era. The goal of my research program is to develop ideas that will allow a deeper understanding of the quantum nature of gravity as it applies to the very early universe, and the very late stages of black hole evolution. The framework I propose is one in which it is possible to simulate using a computer the evolution of quantum states describing configurations of matter and geometry.