A covariant path-integral formulation of the Postquantum theory of classical gravity (PQG) has just been published in Physical Review X, and a few other related papers have come at the same time.
Are the renormalizability results harder to prove when you're coupling postquantum gravity to renormalizable matter? Including matter you see issues for quantum gravity even at one loop, so I'd think you would at least be able to show that the first new Lagrangian term is postponed compared to quantum gravity.
Covariance does not yet resolve the problem of the theory’s full consistency. Renormalization is a very good example.
Still, the approach is quite ingenious: treating the problem in terms of spacetime geometry coupled to quantum matter, rather than simply quantizing gravity itself, which is, after all, built on the “geometry of spacetime.”
I am not convinced, however, particularly by the attempt to explain phantom cold dark matter through stochastic deviations from the standard Hamiltonian constraint surface. This is where, I think, you may have let the argument run a little ahead of the evidence.
Does "classical spacetime coupling with quantum matter" mean that the theory posits an euclidean spacetime that is the fundamental background rather than emergent?
No, it's not Euclidean. Going to Euclidean space gives you the thermal state, while this is a dynamical classical system (the action is called "Onsager-Machlup" or "MSR" etc. (see the image). It's more akin to the path integral for Brownian motion, in comparison the final thermal equilibrium state, although you may reach the thermal state eventually.
Are the renormalizability results harder to prove when you're coupling postquantum gravity to renormalizable matter? Including matter you see issues for quantum gravity even at one loop, so I'd think you would at least be able to show that the first new Lagrangian term is postponed compared to quantum gravity.
Covariance does not yet resolve the problem of the theory’s full consistency. Renormalization is a very good example.
Still, the approach is quite ingenious: treating the problem in terms of spacetime geometry coupled to quantum matter, rather than simply quantizing gravity itself, which is, after all, built on the “geometry of spacetime.”
I am not convinced, however, particularly by the attempt to explain phantom cold dark matter through stochastic deviations from the standard Hamiltonian constraint surface. This is where, I think, you may have let the argument run a little ahead of the evidence.
Does "classical spacetime coupling with quantum matter" mean that the theory posits an euclidean spacetime that is the fundamental background rather than emergent?
No, it's not Euclidean. Going to Euclidean space gives you the thermal state, while this is a dynamical classical system (the action is called "Onsager-Machlup" or "MSR" etc. (see the image). It's more akin to the path integral for Brownian motion, in comparison the final thermal equilibrium state, although you may reach the thermal state eventually.