  1+3 covariant approach to cosmological perturbation theory often employs the
electric part ($E_{ab}$), the magnetic part ($H_{ab}$) of the Weyl tensor or
the shear tensor ($\sigma_{ab}$) in a phenomenological description of
gravitational waves. The Cotton-York tensor is rarely mentioned in connection
with gravitational waves in this approach. This tensor acts as a source for the
magnetic part of the Weyl tensor which should not be neglected in studies of
gravitational waves in the 1+3 formalism. The tensor is only mentioned in
connection with studies of 'silent model' but even there the connection with
gravitational waves is not exhaustively explored. In this study, we demonstrate
that the Cotton-York tensor encodes contributions from both electric, magnetic
part of the Weyl tensor and in directly from the shear tensor. In our opinion,
this makes the Cotton-York tensor arguably the natural choice for linear
gravitational waves in the 1+3 covariant formalism. The tensor is cumbersome to
work with but that should negate its usefulness. It is conceivable that the
tensor would equally be useful in the metric approach, although we have not
demonstrated this in the current study. We contend that the use of only one of
the Weyl tensor or the shear tensor, although phenomenologically correct, leads
to loss of information. Such information is vital particularly when examining
the contribution of gravitational waves to the anisotropy of an almost
-Friedmann-Lamitre-Robertson-Walker (FLRW) universe. The recourse to this loss
is the use Cotton-York tensor.
