The method of the kernel of the evolution equation in the theory of gravity

Abstract: The method of covariant perturbation theory allowed for the computation of the kernel of the evolution equation on a spin Riemannian manifold. The proposed axiomatic definition of the covariant effective action introduces the universal scale parameter, with the length square dimensionality, into a dimensionless mathematical theory. It is shown that this geometrical result has a physical meaning of the action of field theory, including gravity. Two lowest tensor order terms of this functional are independent of a spin group and local. They reproduce the action of general relativity with the cosmological constant. The current value of the universal scale can be determined with the measured Hubble constant. This scale parameter considered as a physical variable can let us build cosmological theories axiomatically.