  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.
