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How universe evolves with cosmological and gravitational constants

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 $g_{\rm ir}\gtrsim 0$ and ultraviolet-stable fixed point $g_{\rm uv}\approx 4/3$ of the gravitational gauge coupling $g=(4/3)G/G_{\rm Newton}$. 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 $Λ\propto ξ^{-2}$. The correlation length $ξ$ characterizes an infrared size of a causally correlate patch of the universe. The cosmological constant $Λ$ 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 $\ell_{\rm pl}$, the universe undergoes inflation in the domain of the ultraviolet-unstable fixed point $g_{\rm ir}$, then evolves to the low-redshift universe in the domain of ultraviolet-stable fixed point $g_{\rm uv}$. We give the quantitative description of the low-redshift universe in the scaling-invariant domain of the ultraviolet-stable fixed point $g_{\rm uv}$, and its deviation from the $Λ$CDM can be examined by low-redshift $(z\lesssim 1)$ cosmological observations, such as supernova Type Ia.