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In a previous work [arXiv:2009.03428] we proposed a new model for QuantumGRavity(QGR) and cosmology, dubbed $SU(\infty)$-QGR. One of the axioms of thismodel is that Hilbert spaces of the Universe and its subsystems represent$SU(\infty)$ symmetry group. In this framework, the classical spacetime isinterpreted as being the parameter space characterizing states of the$SU(\infty)$ representing Hilbert spaces. Using quantum uncertainty relations,it is shown that the parameter space - the spacetime - has a 3+1 dimensionalLorentzian geometry. Here after a review of $SU(\infty)$-QGR, including thedemonstration that its classical limit is Einstein gravity, we compare it withseveral QGR proposals, including: string and M-theories, loop quantum gravityand related models, and QGR proposals inspired by holographic principle andquantum entanglement. The purpose is to find their common and analogousfeatures, even if they apparently seem to have different roles andinterpretations. The hope is that such exercise gives a better understanding ofgravity as a universal quantum force and clarifies the physical nature of thespacetime. We identify several common features among the studied models:importance of 2D structures; algebraic decomposition to tensor products;special role of $SU(2)$ group in their formulation; necessity of a quantum timeas a relational observable. We discuss how these features can be considered asanalogous in different models. We also show that they arise in $SU(\infty)$-QGRwithout fine-tuning, additional assumptions, or restrictions.

Comparing Quantum Gravity Models: String Theory, Loop Quantum Gravity, and Entanglement gravity versus $SU(\infty)$-QGR