Quantum field theory on a cosmological, quantum space-time

Understand

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.