The Cosmological Constant Problem and Quantum Spacetime Reference Frame

TL;DR

This paper proposes a quantum spacetime reference frame model that predicts a cosmological constant close to observations, introduces an effective Einstein-Hilbert term, and suggests testable quantum effects in cosmic redshift variance.

Contribution

It generalizes quantum clock time to a quantum spacetime reference frame using a bosonic non-linear sigma model, deriving novel predictions about dark energy and quantum gravitational effects.

Findings

Predicted cosmological constant near current observational values

Derived an effective Einstein-Hilbert action from quantum spacetime considerations

Identified a universal quantum variance ratio in spacetime intervals

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.