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General Relativity and Quantum Cosmology

Title: The Cosmological Constant Problem and Quantum Spacetime Reference Frame

Authors: M.J.Luo
Abstract: This paper is a generalization of earlier papers [Nucl. Phys. B 884, 344 (2014) (arXiv:1312.2759) and JHEP 6, 63 (2015) (arXiv:1401.2488)]. We generalize the idea of quantum clock time to quantum spacetime reference frame via physical realization of a reference system by quantum rulers and clocks. Omitting the internal degrees of freedom (such as spins) of the physical rulers and clocks, only considering their metric properties, the spacetime reference frame is described by a bosonic non-linear sigma model (NLSM). We study the quantum behavior of the system under approximations, and obtain (1) a cosmological constant valued $(2/\pi)\rho_{c0}$ ($\rho_{c0}$ the critical density at near current epoch) which is very close to the observations; (2) an effective Einstein-Hilbert term; (3) the ratio of variance to mean-squared of spacetime interval tends to a universal constant $2/\pi$ in the infrared region. This effect is testable by observing a linear dependence between the inherent quantum variance and mean-squared of the redshifts from cosmic distant spectral lines. The proportionality is expected to be the observed percentage of the dark energy. The equivalence principle is also generalized to the quantum level.
Comments: 15 pages; v4: updated to the published version in IJMPD, interpretation of NLSM being a theory of spacetime reference frame improved, running dimension in renormalization of NLSM and asymptotic safety formally demonstrated, limitations discussed, refs. added
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph)
Journal reference: Int. J. Mod. Phys. D Vol.27(2018)1850081
DOI: 10.1142/S0218271818500815
Cite as: arXiv:1507.08755 [gr-qc]
  (or arXiv:1507.08755v4 [gr-qc] for this version)

Submission history

From: M.J. Luo [view email]
[v1] Fri, 31 Jul 2015 05:19:58 GMT (18kb)
[v2] Sun, 15 Nov 2015 07:40:49 GMT (20kb)
[v3] Fri, 20 May 2016 02:37:38 GMT (22kb)
[v4] Mon, 19 Mar 2018 07:42:49 GMT (25kb)