Propagation of quantum gravity-modified gravitational waves on a classical FLRW spacetime
Journal
Physical Review D
ISSN
2470-0010
2470-0029
Date Issued
2021
Author(s)
Garcia-Chung, Angel
Mertens, James B.
Rastgoo, Saeed
Tavakoli, Yaser
Vargas Moniz, Paulo
Type
text::journal::journal article
Abstract
The linearized Einstein field equations provide a low-energy wave equation for the propagation of gravitational fields which may originate from a high-energy source. Motivated by loop quantum gravity, we propose the polymer quantization scheme to derive the effective propagation of such waves on a classical Friedmann-Lemaître-Robertson-Walker spacetime. To overcome the challenge of polymer quantizing a time-dependent Hamiltonian, we rewrite such a Hamiltonian in a time-independent manner in the extended phase space, polymerize it, and then transform it back to the usual phase space. In this way, we obtain a time-dependent polymer Hamiltonian for the gravitational waves. We then derive the effective equations of motion and show that (i) the form of the waves is modified, (ii) the speed of the waves depends on their frequencies, and (iii) quantum effects become more apparent as waves traverse longer distances.