  Compact groups (CGs) of galaxies are defined as isolated and dense galaxy
systems that appear to be a unique site of multiple galaxy interactions.
Semi-analytical models of galaxy formation (SAMs) are a prime tool to
understand CGs. We investigate how the frequency and the three-dimensional
nature of CGs depends on the SAM and its underlying cosmological parameters.
Extracting 9 lightcones of galaxies from 5 different SAMs and selecting CGs as
in observed samples, we find that the frequency and nature of CGs depends
strongly on the cosmological parameters. Moving from the WMAP1 to the WMAP7 and
Planck cosmologies (increasing density of the Universe and decreasing
normalisation of the power spectrum), the space density of CGs is decreased by
a factor 2.5, while the fraction of CGs that are physically dense falls from 50
to 35 percent. The lower $\sigma_8$ leads to fewer dense groups, while the
higher $\Omega_{\rm m}$ causes more chance alignments. However, with increased
mass and spatial resolution, the fraction of CGs that are physically dense is
pushed back up to 50 percent. The intrinsic differences in the SAM recipes also
lead to differences in the frequency and nature of CGs, particularly those
related to how SAMs treat orphan galaxies. We find no dependence of CG
properties on the flux limit of the mock catalogues nor on the waveband in
which galaxies are selected. One should thus be cautious when interpreting a
particular SAM for the frequency and nature of CGs.
