  We analyse the kinematics of cosmological spacetimes with nonzero torsion, in
the framework of the classical Einstein-Cartan gravity. After a brief
introduction to the basic features of spaces with non-vanishing torsion, we
consider a family of observers moving along timelike worldlines and focus on
their kinematic behaviour. In so doing, we isolate the irreducible variables
monitoring the observers' motion and derive their evolution formulae and
associated constraint equations. Our aim is to identify the effects of
spacetime torsion, and the changes they introduce into the kinematics of the
standard, torsion-free, cosmological models. We employ a fully geometrical
approach, imposing no restrictions on the material content, or any a priori
couplings between torsion and spin. Also, we do not apply the familiar
splitting of the equations, into a purely Riemannian component plus a
torsion/spin part, at the start of our study, but only introduce it at the very
end. With the general formulae at hand, we use the Einstein-Cartan field
equations to incorporate explicitly the spin of the matter. The resulting
formulae fully describe the kinematics of dynamical spacetimes within the
framework of the Einstein-Cartan gravity, while in the special case of the
so-called Weyssenhoff fluid, they recover results previously reported in the
literature.
