The time-dependent creation and annihilation operators for a complex scalar field, in a Friedmann space-time, defining particle states with respect to which the Hamiltonian is diagonal, are related by a Bogoliubov transformation to the creation and annihilation operators defined in strict analogy with the procedure carried out in Minkowski space. The Bogoliubov transformation is here written in terms of a unitary operator,U, and an expression for that operator is found via the generating functionF=i InU. The properties of the representation obtained by makingU act upon the state vector ❘Ψ〉, to give a new state ❘ΨU〉, are discussed. It is shown that the particle-number operator remains constant in such a picture so that the evolution of the system with time is clearly seen to depend upon the energy ωk on the one hand, and upon the state vector ❘ΨU〉 on the other. Also, it is pointed out that this new representation permits the “in” and “out” states to be defined unambiguously.