We propose a phenomenological generalization of the models of large-scale s
tructure formation in the Universe by gravitational instability in two ways
: we include pressure forces to model multi-streaming, and noise to model f
luctuations due to neglected short-scale physical processes. We show that p
ressure gives rise to a viscous-like force of the same character as the one
introduced in the adhesion model, while noise leads to a roughening of the
density field, yielding a scaling behavior of its correlations.