Quantum Gravity, Quantum Cosmology and Classical Gravity

Abstract

AbstractThe first nine chapters of this monograph deal mainly with quantum cosmology, where some mathematical techniques used in quantum gravity are applied so as to get a better understanding of the early universe. It is therefore very important to discuss and clarify some basic points about the problem of quantum gravity at the beginning of our work. In our opinion, the two main motivations for studying quantum gravity are the following: (a) The singularity theorems of Penrose, Hawking and Geroch show that Einstein’s general relativity leads to the occurrence of singularities in cosmology in a rather generic way (Geroch 1966–1967, Hawking 1966a–b, Hawking 1967, Hawking and Penrose 1970, Hawking and Ellis 1973). One might define the quantum gravity era as the one when all physics is confined to a region whose linear size is of the order of 10−33 cm. In other words we are asking the questions: is there a theory which describes gravitational interactions at these length scales? Does this theory avoid singularities in a generic way? (b) The electroweak and strong interactions are described by renormalizable quantum field theories (Warr 1988). However, Einstein’s general relativity cannot be renormalized (Duff 1982). Some authors (De Witt 1964) tried to rearrange and sum infinite subclasses of Feynman graphs, but in so doing the effective propagators may be shown to pick up new poles which destroy unitarity (Warner 1982). KeywordsQuantum GravityQuantum CosmologyClassical GravityLocal Boundary ConditionGauge ModeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.