  We present a simplified description of expansionistic life in the standard
relativistic cosmology. The resulting model is exactly integrable, yielding a
simple set of predictive formulas. This allows one to quickly propose new
scenarios for the life appearance rate and the dominant expansion speed and
evaluate the observable consequences. These include the expected number and
angular size of visible expanding domains, the total eclipsed fraction of the
sky, and the life-saturated fraction of the universe. We also propose a simple
anthropic bound on observable quantities, as a function of the dominant
expansion velocity alone. The goal is to create a simple and intuition-building
tool for use in the context of cosmology, extragalactic SETI, and futures
studies. We discuss the general predictions of this framework, including
conditions giving rise to an "extragalactic Fermi paradox," in which zero
civilizations are visible beyond the Milky Way. This can occur even if a
substantial fraction of the universe is already saturated with ambitious life.
