How universe evolves with cosmological and gravitational constants

TL;DR

This paper develops a quantum gravitational model with varying constants, describing universe evolution from inflation to low-redshift cosmology, linking fixed points of gravitational coupling to observable cosmological parameters.

Contribution

It introduces a regularized Einstein-Cartan theory with fixed points for gravitational coupling, connecting quantum gravity with cosmological evolution and observable deviations from standard models.

Findings

Universe undergoes inflation near the ultraviolet-unstable fixed point.

Low-redshift universe described by scaling-invariant domain of the ultraviolet-stable fixed point.

Deviations from $ m ext{Lambda CDM}$ can be tested with supernova observations.

Abstract

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.