Aspects of the polynomial affine model of gravity in three dimensions

TL;DR

This paper reformulates the three-dimensional polynomial affine gravity model without a metric, analyzes truncated sectors of the affine connection, and explores cosmological solutions and metric emergence.

Contribution

It introduces a reformulation of the 3D polynomial affine gravity model and analyzes its truncated sectors with cosmological solutions.

Findings

Different kinds of metrics can emerge from the affine connection

Cosmological solutions are identified within truncated sectors

The model provides insights into metric emergence without explicit metric use

Abstract

The polynomial affine gravity is a model that is built up without the explicit use of a metric tensor field. In this article we reformulate the three-dimensional model and, given the decomposition of the affine connection, we analyse the consistently truncated sectors. Using the cosmological ansatz for the connection, we scan the cosmological solutions on the truncated sectors. We discuss the emergence of different kinds of metrics.