  We show how gauge-invariant cosmological perturbations may be constructed by
an unambiguous choice of hypersurface-orthogonal time-like vector field (i.e.,
time-slicing). This may be defined either in terms of the metric quantities
such as curvature or shear, or using some matter field. As an example, we show
how linear perturbations in the covariant fluid-flow approach can then be
presented in an explicitly gauge-invariant form in the coordinate based
formalism.
