The Method of the Kernel of the Evolution Equation in the Theory of Gravity

Abstract

Covariant perturbation theory allows one to calculate the nonlocal kernel of the evolution equation on a spin Riemannian manifold. The proposed axiomatic definition of effective action introduces a universal scale parameter with the dimension of the square of the distance into the dimensionless mathematical theory. It is shown that this purely geometric result has the physical meaning of the action of field theory, including gravity. The two lowest tensor orders of this covariant functional are independent of the type of the spin group and are local; they reproduce the action of general relativity with a cosmological constant. The modern value of the universal distance scale can be determined by the measured Hubble constant. This scale parameter, considered a physical variable, makes it possible to construct the cosmological theory axiomatically.