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

TL;DR

This paper introduces a covariant perturbation method to derive a universal scale parameter in gravity theories, linking geometric functional analysis with physical action, including general relativity and cosmology.

Contribution

It proposes an axiomatic covariant effective action incorporating a universal scale, connecting geometric functional analysis with physical gravity theories.

Findings

Reproduces Einstein-Hilbert action with cosmological constant

Identifies a universal scale parameter linked to the Hubble constant

Provides a basis for axiomatic cosmological theories

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.