Effective equations for isotropic quantum cosmology including matter

Abstract

Effective equations often provide powerful tools to develop a systematic understanding of detailed properties of a quantum system. This is especially helpful in quantum cosmology where several conceptual and technical difficulties associated with the full quantum equations can be avoided in this way. Here, effective equations for Wheeler-DeWitt and loop quantizations of spatially flat, isotropic cosmological models sourced by a massive or interacting scalar are derived and studied. The resulting systems are remarkably different from that given for a free, massless scalar. This has implications for the coherence of evolving states and the realization of a bounce in loop quantum cosmology.

Critical Behaviour in Quantum Gravitational Collapse

“…This is the approach we take. Similar methods has been used to derive effective equations in loop quantum cosmology, 23 and partly form the motivation for our work.…”

“…Comparing this with (23), and using the Poisson bracket commutator correspondence i { , } ↔ [ , ] gives L = √ 2l P , where l P is the Planck length. There are similar operator definitions for the canonical pair (φ, P φ ).…”

Effective Constraints for Quantum Systems

“…Such solvable systems can then be used as the basis for a perturbation theory to analyze more general systems, just like free quantum field theory provides a solvable basis for interacting ones. In quantum cosmology, this is developed in [17,18,19]. Moreover, semiclassical and some other regimes allow one to decouple and truncate the equations consistently, resulting in a finite set of ordinary differential equations.…”

Loop quantum gravity corrections to gravitational wave dispersion

“…If a matter potential or anisotropies and inhomogeneities are added, additional corrections arise [29] from quantum back-reaction.…”