The Cosmological Constant Problem and Quantum Spacetime Reference Frame

Abstract

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. We study the quantum behavior of the system under approximations, and obtain (1) a cosmological constant valued (2/π)ρc0 (ρc0 the critical density at near current epoch) which is very close to the observations; (2) an effective Einstein-Hilbert term in the effective action; (3) the ratio of variance to mean-squared of spacetime interval tends to a universal constant 2/π 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. We also generalize the equivalence principle to be valid for all quantum phenomenon.

Local Conformal Instability and Local Non-Collapsing in the Ricci flow of Quantum Spacetime

“…[20][21][22][23][24][25][26][27][28]). In our previous works (motivation and logical derivation will be reviewed in the appendix of the paper), we have tried to lay a solid physical foundation for the spacetime Ricci flow based on a well-defined relativistic quantum fields theory of spacetime reference frame [29][30][31][32][33][34][35], in which the Ricci flow arises as the RG flow of quantum spacetime at the gaussian approximation. It seens that several foundamental issues of quantum gravity are consistently treated within the frameworks, e.g.…”