Maximal symmetry and metric-affine f(R) gravity

TL;DR

This paper investigates the structure of metric-affine f(R) gravity with maximally symmetric spatial subspaces, deriving the connection properties, reducing degrees of freedom, and comparing cosmological equations in different formalisms.

Contribution

It derives the affine connection in maximally symmetric spaces within metric-affine f(R) gravity, reducing degrees of freedom and contrasting the resulting Friedmann equations in different formalisms.

Findings

The affine connection is explicitly derived for maximally symmetric subspaces.

The degrees of freedom in metric-affine gravity are significantly reduced.

Friedmann equations differ between Palatini and metric-affine formalisms in the presence of matter.

Abstract

The affine connection in a space-time with a maximally symmetric spatial subspace is derived using the properties of maximally symmetric tensors. The number of degrees of freedom in metric-affine gravity is thereby considerably reduced while the theory allows spatio-temporal torsion and remains non-metric. The Ricci tensor and scalar are calculated in terms of the connection and the field equations derived for the Einstein-Hilbert as wells as for f(R) Lagrangians. By considering specific forms of f(R), we demonstrate that the resulting Friedmann equations in Palatini formalism without torsion and metric-affine formalism with maximal symmetry are in general different in the presence of matter.