Houri Ziaeepour

$SU(\infty)$-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 $Ξ$. Nonetheless, physical processes and measurables must be independent $Ξ$'s geometry. In previous works we demonstrated that diffeomorphism of $Ξ$ 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.