Percolation of 'Mortal Civilisation' in an FLRW universe

Abstract In this work, we study the percolation of `mortal civilisation' through an effectively uniform distribution of planets embedded in an expanding background spacetime. The corresponding homogeneous and isotropic universes include matter-dominated and dark energy-dominated universes, with the static universe as their common limit. Restricting our attention to causal spherical regions of these universes, we find that even with the combined effects of mortality factor and background expansion, the behaviour of the occupation of planets effectively follow the Logistic Growth Model. In addition to this, we discover three-parameter fitting equations describing the total percolation time as a function of the Hubble expansion rate of the universe and death rate of the spreading `civilisation'. Interestingly, these fitting equations may be reduced to one-parameter models in cases where the occupation of the spherical region is limited to a few percent less than its total planet population. These equations have a further consequence that a percolation of `mortal civilisation' in a static universe has an exponential mapping to the spread of `immortal civilisation' in a dark energy dominated-universe. Our three-parameter models and the logistic growth fitting equations break down when the planets at the boundary of spherical region goes off beyond the Hubble horizon due to extremely fast background expansion in a dark energy-dominated universe.