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

Abstract

$SU(\infty)$ Quantum GRavity (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 $Ξ$. Nonetheless, physical processes and measurables must be independent of the geometry of $Ξ$. In previous works we demonstrated that diffeomorphism of $Ξ$ can be neutralized by $SU(\infty)$ gauge transformation. In this work we show that the invariance of action under variation of $Ξ$'s metric 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 (HSF) on the emergent classical spacetime and different cosmological era, such as inflation, reheating, and late time accelerating expansion. The results of this preliminary and approximate investigation show that HSF may be classically interpreted as these phenomena. Consequently, inflaton, quintessence, and similar fields associated to these processes may be order parameters that phenomenologically present them.