How universe evolves with cosmological and gravitational constants

Understand

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.