the modes among themselves and with the minisuperspace degrees of freedom are being ignored. It is also well-known that this truncation violates the uncertainty principle, since it implies setting the amplitudes and momenta of the inhomogeneous modes simultaneously to zero. It is therefore important to understand under what conditions it is reasonable to consider an autonomous evolution of the minisuperspace wave function ignoring the truncated degrees of freedom. Misner was keenly aware of the problems when he introduced this approximation. The first attempt to actually assess the validity of the minisuperspace approximation was made only recently by Kuchar and Ryan (1986, 1989).

Two of us (Sinha and Hu 1991) have tried to address this question in the context of interacting field theory with the help of the coarse-grained effective action method mentioned above. The model considered is that of a self interacting (${\lambda \phi^{4}}$) scalar field coupled to a closed Robertson Walker background spacetime. The “system”(minisuperspace) consists of the scale factor $a$ and the lowest mode of the scalar field, while the “environment" consists of the inhomogeneous modes. [^4] In this model calculation the scalar field is mimicking the inhomogeneous gravitational degrees of freedom in superspace. We are motivated to 