Energy-momentum and dark energy in $\boldsymbol{SU(\infty)}$-QGR quantum gravity

TL;DR

This paper explores an $SU( olinebreak ext{infinity})$-QGR quantum gravity model, deriving Einstein-like constraints and analyzing quantum information effects on cosmological phenomena such as inflation and acceleration.

Contribution

It introduces a novel quantum gravity framework with $SU( ext{infinity})$ symmetry, deriving Einstein-like equations and linking quantum state evolution to cosmological dynamics.

Findings

Derived Einstein-like equations from $SU( ext{infinity})$ symmetry invariance.

Quantum information measures reveal effects of Hilbert space fragmentation on spacetime evolution.

Fields related to inflation and acceleration act as order parameters of quantum states.

Abstract

$SU(\infty)$-QGR is a recently proposed fundamentally quantum approach to gravity and cosmology. In this model the Hilbert space of the Universe represents $SU(\infty)$ symmetry. Its fragmentation generates approximately isolated subsystems (particles) representing, in addition to $SU(\infty)$, finite-rank local symmetries. The common $SU(\infty)$ is associated to quantum gravity, and at lowest quantum order the effective action for all symmetries is Yang-Mills on a 4D parameter space $\Xi$. Nonetheless, physical processes and measurables must be independent $\Xi$'s geometry. In previous works we demonstrated that diffeomorphism of $\Xi$ can be neutralized by $SU(\infty)$ gauge transformation. In this work we show that invariance of action under metric change leads to a constraint resembling Einstein equation. It consists of energy-momentum tensors for all components of the model, including the spin-1 gravitons. In addition, through calculation of quantum information measures we study the effect of Hilbert space fragmentation on the evolution of emergent classical spacetime and cosmological phenomena, namely inflation and late time accelerating expansion. The results show that fields associated to these processes may be order parameters collectively presenting the evolution of quantum states of the contents of the Universe.