Problem of Time in Slightly Inhomogeneous Cosmology (1403.7583v4)

Abstract: The Problem of Time (PoT) is a multi-faceted conceptual incompatibility between various areas of Theoretical Physics. Whilst usually stated as between GR and QM, in fact 8/9ths of it is already present at the classical level. Thus we adopt a top-down' classical and then quantum approach. I consider a local resolution to the Problem of Time that is Machian, which was previously realized for relational triangle and minisuperspace models. This resolution has three levels: classical, semiclassical and combined semiclassical-histories-records. This article's specific model is a slightly inhomogeneous cosmology considered for now at the classical level. This is motivated by how the inhomogeneous fluctuations that underlie structure formation - galaxies and CMB hotspots - might have been seeded by quantum cosmological fluctuations, as magnified by some inflationary mechanism. In particular, I consider the perturbations about $S^3$ case of this involving up to second order, which has a number of parallels with the Halliwell-Hawking model but has a number of conceptual differences and useful upgrades. The article's main features are that the elimination part of the model's thin sandwich is straightforward, but the modewise split of the constraints fail to be first-class constraints. Thus the elimination part only arises as an intermediate geometry between superspace and Riem. The reduced geometries have surprising singularities influenced by the matter content of the universe, though the N-body problem anticipates these with its collinear singularities. I also give abasis set' of Kuchar beables for this model arena.