Cosmological solutions to polynomial affine gravity in the torsion-free sector
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.
Keywords
Cite
@article{arxiv.1808.05970,
title = {Cosmological solutions to polynomial affine gravity in the torsion-free sector},
author = {Oscar Castillo-Felisola and José Perdiguero and Oscar Orellana},
journal= {arXiv preprint arXiv:1808.05970},
year = {2019}
}
Comments
V2: 14 pages, bibliography corrected. Accepted as a chapter for the book "Redefining Standard Model Cosmology" to be published by IntechOpen