Renormalizability of a fully quantum theory reproducing the stochastic effects

Develop a renormalisable fully quantum theory of gravity (or effective theory) that reproduces the large stochastic spacetime fluctuations and associated phenomenology identified by the classical-quantum framework, specifying the renormalisation scheme and demonstrating consistency with observed constraints.

Background

Although the paper’s formalism treats the metric as classical with stochastic dynamics, the authors note the possibility that similar phenomenology could emerge from a fully quantum theory of gravity viewed as an effective model. They regard this as unlikely but do not rule it out.

They explicitly state that, even if such a fully quantum effective description exists, they currently do not know how to render it renormalisable. Addressing this would clarify whether the observed low-acceleration anomalies can be embedded within a quantum framework.