  In general, the laws of physics are not invariant under a change of scale. To
find out whether the 'scale-invariance hypothesis' corresponds to nature or
not, a careful examination to its implications is required. As a consequence,
the scale-invariance cosmological models need to be carefully checked with many
tests in order to confirm or disconfirm them. In this paper, three different
toy models have been introduced in the framework of a scale-invariance
cosmology to examine dark energy and cosmic transit. Although cosmic transit
exists in the three models, the pressure stays always negative during cosmic
evolution. In addition, there is always a singularity in the evolution of the
equation of state parameter which is not suitable for a complete investigation
of dark energy evolution. The undesirable features of the parameters have been
discussed, and a comparison with other cosmological contexts has been done.
