A polynomial affine model of gravity: after ten years

Abstract

The polynomial affine model of gravity was proposed as an alternative to metric and metric-affine gravitational models. What at the beginning was thought as a source of unpredictability, the presence of many terms in the action, turned out to be a milestone, since it contains all possible combinations of the fields compatible with the covariance under diffeomorphisms. Here, we present a review of the advances in the analysis of the model after ten years of its proposal, and sketch the guideline of our future perspectives.