Polynomial affine gravity in 3+1 dimensions

TL;DR

This paper explores polynomial affine gravity in 3+1 dimensions, an alternative to Einstein's theory, where the affine connection is fundamental and metric properties may emerge, with implications for cosmological models.

Contribution

It introduces a finite-term polynomial affine gravity model in 3+1 dimensions, generalizing Einstein's equations without fundamental metrics, and discusses emergent metric fields and cosmological solutions.

Findings

Coupling constants are dimensionless.

The action involves a finite number of terms.

Emergent metric tensor fields are possible from the connection.

Abstract

The polynomial affine gravity is an alternative model of gravity whose fundamental field is the affine connection, and it is invariant under the complete group of diffeomorphisms. In 3+1 dimensions the field equations generalise those of Einstein--Hilbert, the coupling constants are dimensionless, the action has a finite numbers of term, and although the action does not involve a (fundamental) metric, some metric tensor fields might \emph{emerge} from the connection. Provided a cosmological ansatz, the properties of diverse cosmological models are discussed.