# Beyond Einstein: A Polynomial Affine Model of Gravity

## TL;DR

This paper introduces a polynomial affine gravity model that admits Einstein manifolds as solutions, connects to a Yang-Mills gravity theory, and extends scalar field concepts within an affine framework.

## Contribution

It demonstrates that the polynomial affine gravity model encompasses Einstein solutions and relates to SKY theory, offering new avenues for understanding gravity and scalar fields.

## Key findings

- Einstein manifolds are solutions in the affine model.
- The effective equations relate to SKY gravity theory.
- A generalization of scalar fields within the affine framework.

## Abstract

We show that the effective field equations for a recently formulated polynomial affine model of gravity, in the sector of a torsion-free connection, accept general Einstein manifolds---with or without cosmological constant---as solutions. Moreover, the effective field equations are partially those obtained from a gravitational Yang-Mills theory known as the Stephenson-Kilmister-Yang (SKY) theory. Additionally, we find a generalisation of a minimally coupled massless scalar field in general relativity within a "minimally" coupled scalar field in this affine model. Finally, we present the road map to finding general solutions to the effective field equations with either isotropic or cosmologic (i.e., homogeneous and isotropic) symmetry.