How universe evolves with cosmological and gravitational constants

With a basic varying space–time cutoff ℓ˜, we study a regularized and quantized Einstein–Cartan gravitational field theory and its domains of ultraviolet-unstable fixed point gir≳0gir≳0 and ultraviolet-stable fixed point guv≈4/3guv≈4/3 of the gravitational gauge coupling g=(4/3)G/GNewtong=(4/3)G/GNewton. 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∝ξ−2Λ∝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 ℓ˜ decreases and approaches to the Planck length ℓplℓpl, the universe undergoes inflation in the domain of the ultraviolet-unstable fixed point girgir, then evolves to the low-redshift universe in the domain of ultraviolet-stable fixed point guvguv. We give the quantitative description of the low-redshift universe in the scaling-invariant domain of the ultraviolet-stable fixed point guvguv, and its deviation from the ΛCDM can be examined by low-redshift (z≲1)(z≲1) cosmological observations, such as supernova Type Ia.