We present a solution to the cosmological constant, the zero-point energy,and the quantum gravity problems within a single comprehensive framework. Weshow that in quantum theories of gravity in which the zero-point energy densityof the gravitational field is well-defined, the cosmological constant andzero-point energy problems solve each other by mutual cancellation between thecosmological constant and the matter and gravitational field zero-point energydensities. Because of this cancellation, regulation of the matter fieldzero-point energy density is not needed, and thus does not cause any traceanomaly to arise. We exhibit our results in two theories of gravity that arewell-defined quantum-mechanically. Both of these theories are locally conformalinvariant, quantum Einstein gravity in two dimensions and Weyl-tensor-basedquantum conformal gravity in four dimensions (a fourth-order derivative quantumtheory of the type that Bender and Mannheim have recently shown to beghost-free and unitary). Central to our approach is the requirement that anyand all departures of the geometry from Minkowski are to be brought about byquantum mechanics alone. Consequently, there have to be no fundamentalclassical fields, and all mass scales have to be generated by dynamicalcondensates. In such a situation the trace of the matter field energy-momentumtensor is zero, a constraint that obliges its cosmological constant andzero-point contributions to cancel each other identically, no matter how largethey might be. Quantization of the gravitational field is caused by itscoupling to quantized matter fields, with the gravitational field not needingany independent quantization of its own. With there being no a priori classicalcurvature, one does not have to make it compatible with quantization.
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