The Probability of a Galaxy Already Colonized, Assuming FTL (Warp), and Comparison with speed of light or sublight models

We reorient the analysis of the Fermi paradox towards a central question: if the principle of warp travel (FTL, Faster-Than-Light) could have been discovered before us, what is the probability that the Milky Way is already colonized? We construct a minimalistic probabilistic model for the emergence of expansionist civilizations and show that, with a full galactic colonization time on the order of tens of thousands of years, the probability of an "empty" Galaxy remains high only if the rate of emergence of expansionist civilizations is less than one per tens of billions of years per galaxy. For comparison, we provide the same estimates for c and sublight speed regimes, demonstrating that FTL amplifies, but does not fundamentally alter, the conclusion: colonization times remain microscopic compared to the age of the Milky Way.