  In this work, we consider the spread of a 'civilisation' in an idealised
homogeneous isotropic universe where all the planets of interest are habitable.
Following a framework that goes beyond the usual idea of percolation, we
investigate the behaviour of the number of colonised planets with time, and the
total colonisation time for three types of universes. These include static,
dark energy-dominated, and matter-dominated universes. For all these types of
universes, we find a remarkable fit with the Logistic Growth Function for the
number of colonised planets with time. This is in spite of the fact that for
the matter- and dark-energy dominated universes, the space itself is expanding.
For the total colonisation time, $T$, the case for a dark energy-dominated
universe is marked with divergence beyond the linear regime characterised by
small values of the Hubble parameter, $H$. Not all planets in a spherical
section of this universe can be 'colonised' due to the presence of a shrinking
Hubble sphere. In other words, the recession speeds of other planets go beyond
the speed of light making them impossible to reach. On the other hand, for a
matter-dominated universe, while there is an apparent horizon, the Hubble
sphere is growing instead of shrinking. This leads to a finite total
colonisation time that depends on the Hubble parameter characterising the
universe; in particular, we find $T\sim H$ for small $H$ and $T\sim H^2$ for
large $H$.
