Cosmological solutions to polynomial affine gravity in the torsion-free sector

TL;DR

This paper explores cosmological models within Polynomial Affine Gravity, revealing that its vacuum solutions include those of General Relativity and that matter effects can be geometrically emulated, with some solutions extending beyond metric-compatible connections.

Contribution

It demonstrates that Polynomial Affine Gravity encompasses General Relativity solutions and introduces a geometric approach to emulate matter effects without explicit matter fields.

Findings

Vacuum solutions of GR are a subset of Polynomial Affine Gravity solutions.

Cosmological constant emerges as an integration constant.

Affine structures can emulate matter effects in cosmology.

Abstract

We find possible cosmological models of the Polynomial Affine Gravity described by connections that are either compatible or not with a metric. When possible, we compare them with those of General Relativity. We show that the set of cosmological vacuum solutions in General Relativity are a subset of the solutions of Polynomial Affine Gravity. In our model the cosmological constant appears as an integration constant, and additionally, we show that some forms of matter can be emulated by the affine structure---even in the metric compatible case. In the case of connections not compatible with a metric, we obtain formal families of solutions, which should be constrained by physical arguments. We show that for a certain parametrisation of the connection, the affine Ricci flat condition yield the cosmological field equations of General Relativity coupled with a perfect fluid, pointing toward a geometrical emulation of---what is interpreted in General Relativity as---matter effects.