How universe evolves with cosmological and gravitational constants

Abstract

With a basic varying space-time cutoff $\tilde{\ell }$, we study a regularized and quantized Einstein-Cartan gravitational field theory and its domains of ultraviolet-unstable fixed point $g_{\mathrm{ir}}\gtrsim 0$ and ultraviolet-stable fixed point $g_{\mathrm{uv}}\approx 4/3$ of the gravitational gauge coupling $g=(4/3)G/G_{\mathrm{Newton}}$. Because the fundamental operators of quantum gravitational field theory are dimension-2 area operators, the cosmological constant is inversely proportional to the squared correlation length $\Lambda \propto {\xi }^{-2}$. The correlation length $\xi$ characterizes an infrared size of a causally correlate patch of the universe. The cosmological constant $\Lambda$ and the gravitational constant $G$ are related by a generalized Bianchi identity. As the basic space-time cutoff $\tilde{\ell }$ decreases and approaches to the Planck length ${\ell }_{\mathrm{pl}}$, the universe undergoes inflation in the domain of the ultraviolet-unstable fixed point $g_{\mathrm{ir}}$, then evolves to the low-redshift universe in the domain of ultraviolet-stable fixed point $g_{\mathrm{uv}}$. We give the quantitative description of the low-redshift universe in the scaling-invariant domain of the ultraviolet-stable fixed point $g_{\mathrm{uv}}$, and its deviation from the $\Lambda$CDM can be examined by low-redshift $(z\lesssim 1)$ cosmological observations, such as supernova Type Ia.

typo corrections, the final version to appear in Nucl. Phys. B (2015). 24 pages and 6 figures

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