Complete background cosmology of parity-even quadratic metric-affine gravity

TL;DR

This paper analyzes the cosmological implications of a general parity-even quadratic metric-affine gravity model, deriving modified Friedmann equations, exploring special solution branches, and providing computational tools for further research.

Contribution

It introduces the complete background cosmology of a general quadratic metric-affine gravity model, including new solution branches and explicit equations for various cosmological geometries.

Findings

Identified a branch screening spatial curvature from field equations.

Found an integrable branch with (anti) de Sitter late-time expansion.

Provided the most general model reproducing Einstein's Friedmann equations.

Abstract

The cosmology of metric-affine gravity is studied for the general, parity preserving action quadratic in curvature, torsion and non-metricity. The model contains 27 a priori independent couplings in addition to the Einstein constant. Linear and higher order relations between the quadratic operators in a Friedmann--Lemaitre--Robertson--Walker spacetime are obtained, along with the modified Friedmann, torsion and non-metricity equations. Extra parameter constraints lead to two special branches of the model. Firstly, a branch is found in which the Riemannian spatial curvature (thought to be slightly closed or flat in the Lambda-CDM model of our Universe) is entirely screened from all the field equations, regardless of its true value. Secondly, an integrable branch is found which yields (anti) de Sitter expansion at late times. The particle spectra of these two branches are studied, and the need to eliminate higher-spin particles as well as ghosts and tachyons motivates further parameter constraints in each case. The most general model is also found which reproduces the exact Friedmann equations of general relativity. The full set of equations describing closed, open or flat cosmologies, for general parity-even quadratic metric-affine gravity, is made available for SymPy, Mathematica and Maple platforms.