期刊
PHYSICAL REVIEW D
卷 103, 期 8, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevD.103.084053
关键词
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资金
- European Cooperation in Science and Technology [CA18108]
- Perimeter Institute for Theoretical Physics
- Government of Canada through the Department of Innovation, Science and Economic Development Canada
- Province of Ontario through the Ministry of Research, Innovation and Science
- FCT at CMA-UBI [UIDBMAT/00212/2020, UIDPMAT/00212/2020]
By applying the polymer quantization scheme, we derived the effective propagation of gravitational waves in a classical spacetime, obtained a time-dependent polymer Hamiltonian, and demonstrated how the form, speed, and quantum effects of the waves change as they travel longer distances.
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-Lemaitre-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.
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