Jean-Philippe Bruenton has made some interesting model-independent predictions in a pre-print regarding the phenomenological laws of quantum gravity. He argues that:
(1) There exists a (theoretically) maximal energy density and pressure.
(2) There exists a mass-dependent (theoretically) maximal acceleration given by mc3/(h bar) if m < mp and by c4/Gm if m > mp. This is of the order of Milgrom's acceleration a0 for ultra-light particles (m approximately H0) that could be associated to the Dark Energy fluid. This suggests models in which modified gravity in galaxies is driven by the Dark Energy field, via the maximal acceleration principle. It follows trivially from the existence of a maximal acceleration that there also exists a mass dependent maximal force and power.
(3) Any system must have a size greater than the Planck length, in the sense that there exists a minimal area (but without implying for quanta a minimal Planckian wavelength in large enough boxes).
(4) Physical systems must obey the Holographic Principle. Holographic bounds can only be saturated by systems with m > mp; systems lying on the "Compton line" "l" approximately equal to 1/m are fundamental objects without substructures
Bruenton's conjectures are driven by observations about the relationships of the Planck length, mass, and time which are derived from the speed of light c, the gravitational force constant G, and the reduced Planck's constant h bar, the Schwarzchild solution for the event horizon of a Black Hole in General Relativity reformulated in a generalized and manifestly covariant way, observations about the Kerr-Newman family of black holes, an alternate derivation of the Heisenberg uncertainty principle, the notion of a Compton length, and a few other established relationships.
Bruenton presents his conclusions as heuristic conjectures for any quantum gravity theory that displays a minimum set of commonly hypothesized features, rather than rigorously proven scientific laws.
I have omitted some of his more technical observations and consolidated others.
Bruenton acknowledges that these observations may fail in the case certain theoretically possible exotic "hairy" black holes (while implying that they probably don't exist for some non-obvious reason). He equivocates on the question of whether Lorentz symmetry violations near the Planck scale are possible, reasoning that an absence of a minimal Planckian wavelength could rescue Lorentz symmetry from quantum gravity effects.
I find his suggestion that there is a maximal energy density and pressure particularly notable because of the remarkable coincidence between the maximum density observed by astronomers in Black Holes and neutron stars on one hand, and the maximum observed density of an atomic nucleus on the other.
His suggestion that the Planck scale my denote the line between systems that are "fundamental objects without substructures" and "physical systems" is also shrewd.