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
$\Lambda\propto \xi^{-2}$. 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 $\ell_{\rm pl}$, 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
$\Lambda$CDM can be examined by low-redshift $(z\lesssim 1)$ cosmological
observations, such as supernova Type Ia.
