Einstein's gravity from a polynomial affine model

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 Stephenson--Kilmister--Yang theory. Additionally, we find a generalization of a minimally coupled massless scalar field in General Relativity within a "minimally" coupled scalar field in this affine model. Finally, we present a brief analysis of the propagators of the gravitational theory, and count the degrees of freedom. For completeness we prove that a Birkhoff-like theorem is valid for the analyzed sector.