Disordered boundaries destroy bulk phase separation in scalar active matter

We show that disordered boundaries destroy bulk phase separation in scalar active systems in dimension d <3. This is in strong contrast with the equilibrium case where boundaries have no impact on the bulk of phase-separated systems. The underlying mechanism is revealed by considering a localized deformation of an otherwise flat wall, from which the case of a disordered boundary can be inferred. We find long-ranged correlations of the density field as well as a cascade of eddies which we show prevent bulk phase separation in low enough dimensions. The results are derived for dilute systems as well as in the presence of interactions, under the sole condition that the density field is the unique hydrodynamic mode.