BornOppenheimer meets WignerWeyl in quantum gravity
Abstract
Starting from a BornOppenheimer decomposition of the WheelerDeWitt equation for the quantum cosmology of the mattergravity system, we have performed a WignerWeyl transformation and obtained equations involving a Wigner function for the scale factor and its conjugate momentum. This has allowed us to study in more detail than previously the approach to the classical limit of gravitation and the way time emerges in such a limit. To lowest order we reproduce the Friedmann equation and the previously obtained equation for the evolution of matter. We also obtain expressions for higher order corrections to the semiclassical limit.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 September 2021
 DOI:
 10.1088/13616382/ac1b0a
 arXiv:
 arXiv:2104.07480
 Bibcode:
 2021CQGra..38r5006K
 Keywords:

 quantum cosmology;
 inflation;
 classical limit;
 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 High Energy Physics  Theory
 EPrint:
 15 pages, no figures