Physicists had followed the following historical broad trajectory regarding quantum field theory on curved spacetime according to Wald-QFT-curved:

The main initial development of the theory occurred in the late 1960’s driven primarily by the desire to analyze the phenomenon of particle creation occurring in the very early universe. By 1969, one can find the theory formulated in recognizably modern form and applied to cosmology in the paper of Parker. In the early 1970’s the theory was applied to the study of particle creation near rotating and charged black holes, where the discovery of classical “superradiant scattering” (analogous to stimulated emission) strongly suggested that spontaneous particle creation should occur. This line of research culminated in the analysis by Hawking of particle creation resulting from gravitational collapse of body to form a black hole. It was thereby discovered that black holes radiate as perfect black bodies at temperature where is the surface gravity of the black hole. This result solidified an undoubtedly deep connection between the laws of black hole physics and the laws of thermodynamics, the ramifications of which continue to be pondered today.

As a direct consequence of Hawking’s remarkable discovery, there occurred in mid-to-late 1970’s a rapid and extensive development of quantum fields in curved spacetime and its applications to a variety of phenomena. A good summary of this body of work can be found in Birrell and Davies. Further important applications to cosmology were made in the early 1980’s as the methods and results of quantum field theory in curved spacetime were used to calculate the perturbations generated by quantum field flctuations during inflation. Many of these lines of investigation begun in late 1970’s and 1980’s continue to be pursued today.

Although it would be more difficult to point to major historic landmarks, during the past twenty years the theoretical framework of quantum field theory on curved spacetime had undergone significant development, mainly through the incorporation of key aspects of the algebraic approach to quantum field theory. As a result the theory of a linear quantum field propagating in a globally hyperbolic spacetime can be formulated in an entirely mathematically rigorous manner insofar as the definition of the fundamental field observables is concerned.

Against this backdrop the question of interest to me is whether if we consider a fixed curved spacetime that is different from Minkowski space, which I believe should be whether the mathematically rigorous quantum field theory for this globally hyperbolic model could simplify quantum field theory itself. My instincts are to suggest that quantum phenomena generally are due to this sort of model of the actual universe and that the mass gap conjecture for Minkowski space should have a negative solution (by Jormakka’s approach say) and we have a mass gap in the actual universe because we live in a compact curved universe where quantum field theory is an overcomplex model and mass gap and other problems are resolved by compactness. This intuition would provide us with simple resolutions of many problems such a thermal equilibrium of cosmic background radiation.