Exponential decay for small nonlinear perturbations of expanding flat homogeneous cosmologies - art. no. 083507.

It is shown that during expanding phases of Bat homogeneous cosmologies all nonlinear perturbations which are small enough are bounded by an exponenti ally decaying function, with the exponent being a (negative) fraction of th e minimum value the Hubble function takes during the expanding period consi dered. When the cosmological constant is negative, i.e.,in our conventions, when there is sustained inflation, it follows that nonlinear perturbations which are small enough decay exponentially; thus, a cosmic no-hair theorem is established. This result holds for a large class of perfect fluid equat ions of state, but notably not for very "stiff" fluids such as the pure rad iation case. [S0556-2821(99)06316-X].