Gauged Gravity via Spectral Asymptotics of non-Laplace type Operators

TL;DR

This paper develops a gauge-invariant spectral theory for non-Laplace type operators on vector bundles, proposing a new matrix-based approach to gravitation that generalizes Einstein's theory.

Contribution

It introduces a novel class of invariant differential operators and spectral invariants that extend gravitational theories beyond Riemannian metrics.

Findings

Spectral invariants are invariant under diffeomorphisms and gauge transformations.

The theory generalizes Einstein gravity to a matrix framework.

Connections with Finsler geometry and Hodge-de Rham theory are established.

Abstract

We construct invariant differential operators acting on sections of vector bundles of densities over a smooth manifold without using a Riemannian metric. The spectral invariants of such operators are invariant under both the diffeomorphisms and the gauge transformations and can be used to induce a new theory of gravitation. It can be viewed as a matrix generalization of Einstein general relativity that reproduces the standard Einstein theory in the weak deformation limit. Relations with various mathematical constructions such as Finsler geometry and Hodge-de Rham theory are discussed.