The Cosmological Constant Problem and Quantum Spacetime Reference Frame

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.

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

References in corpus (7)

• TASI Lectures on the Cosmological Constant
• Fractal properties of quantum spacetime
• Time from quantum entanglement: an experimental illustration
• Fixed Points of Nonlinear Sigma Models in d>2
• The Cosmological Constant Problem and Re-interpretation of Time
• The Weight of Vacuum Fluctuations
• Dark Energy from Quantum Uncertainty of Distant Clock

Cited by in corpus (9)

• Ricci Flow Approach to The Cosmological Constant Problem
• Local Conformal Instability and Local Non-Collapsing in the Ricci flow of Quantum Spacetime
• Trace Anomaly, Perelman's Functionals and the Cosmological Constant
• A Statistical Fields Theory underlying the Thermodynamics of Ricci Flow and Gravity
• Quantum Modified Gravity at Low Energy in the Ricci Flow of Quantum Spacetime
• The Ricci Flow and the Early Universe
• Second-Order Moment Quantum Fluctuations and Quantum Equivalence Principle
• Local Short-Time Acceleration induced Spectral Line Broadening and Possible Implications in Cosmology
• Quantum Mechanics Relative to a Quantum Reference System: a Relative State Approach