Quantum field theory on a cosmological, quantum space-time

Abstract

In loop quantum cosmology, Friedmann-LeMaitre-Robertson-Walker (FLRW) space-times arise as well-defined approximations to specific \emph{quantum} geometries. We initiate the development of a quantum theory of test scalar fields on these quantum geometries. Emphasis is on the new conceptual ingredients required in the transition from classical space-time backgrounds to quantum space-times. These include a `relational time' a la Leibnitz, the emergence of the Hamiltonian operator of the test field from the quantum constraint equation, and ramifications of the quantum fluctuations of the background geometry on the resulting dynamics. The familiar quantum field theory on classical FLRW models arises as a well-defined reduction of this more fundamental theory.

19 pages, no figures; A reference and footnote added, PACs and minor typos corrected; a significant technical clarification added to section IV.A; minor typos corrected; two references added

References in corpus (14)

• Quantum Nature of the Big Bang: Improved dynamics
• Quantum Nature of the Big Bang
• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• Loop quantum cosmology of k=1 FRW models
• Corrections to the Friedmann Equations from LQG for a Universe with a Free Scalar Field
• Loop quantum cosmology and the k = - 1 RW model
• Closed FRW model in Loop Quantum Cosmology
• Anti-deSitter universe dynamics in LQC
• Loop cosmological dynamics and dualities with Randall-Sundrum braneworlds
• Is loop quantization in cosmology unique?
• Quantum bounce and cosmic recall
• Gauge invariant perturbations around symmetry reduced sectors of general relativity: applications to cosmology
• The flat FRW model in LQC: the self-adjointness
• Physical time and other conceptual issues of QG on the example of LQC