preferred slicing as follows. The time-like eigenvector of the stress tensor, which always exists for realistic matter (see pages 89-90 of [@haw]), generates a preferred non-crossing family of world-lines and one can construct, at any given time $t$, a family of hypersurfaces ortogonal to these world-lines, obtaining in this way the so-called [*co-moving slicing*]{}.

Another simple scalar could be obtained by working in the Weitzenböck spacetime (the usual Levi-Civita connection is replaced by the Weitzenböck one) [@w], where torsion does not vanish. In this spacetime, the scalar torsion for synchronous observers in the flat FLRW geometry is equal to minus three times the Hubble parameter, thus satisfying the required property. Unfortunately, as has been shown in [@lsb], this theory is not locally Lorentz invariant.

For this reason, people have kept looking for a really covariant invariant, and have dealt with the Carminati-McLenaghan invariants [@cm; @hp18], with a general function of the Ricci and Gauss-Bonet scalars or with second derivatives of the Riemann tensor [@yoshida]. The problem with these purely gravitational invariants is that they are quite involved and lead to very complicated equations for cosmological perturbations. Moreover, in our approach –not using the principle of the [*limiting curvature hypothesis*]{} considered 