How universe evolves with cosmological and gravitational constants

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