I can't answer your question directly, but I can quote from my handy textbook on General Relativity which admittedly is 30 years old now ('General Relativity', Robert M. Wald, 1984). From Chapter 14, 'Quantum Effects in Strong Gravitational Fields', "As discussed in chapter 9, spacetime singularities occur in the solutions of classical general relativity relevant to gravitational collapse and cosmology. Thus, in these situations, the classical description of spacetime structure must break down. In particular, one cannot expect the homogeneous, isotropic models of chapter 5 to be an adequate description of our universe in the regime where they predict curvature of magnitude Ip^-2 or greater, i.e, t tp ~ 10^-43 s." Ok, I got lost in the definition of Ip there (actually much earlier in the book), but the textbook writers clearly believe that classical GR breaks down at some density/energy limit and gravity then needs a quantum description.

Also, physicists, for reasons I can't state, strongly believe that all physical phenomena are described by quantum theories.