  We consider the functional Schrodinger equation for a self interacting scalar
field in an expanding geometry. By performing a time dependent scale
transformation on the argument of the field we derive a functional Schrodinger
equation whose hamiltonian is time independent but involves a time-odd term
associated to a constraint on the expansion current. We study the mean field
approximation to this equation and generalize in this case, for interacting
fields, the solutions worked out by Bunch and Davies for free fields.
