Quantum evolution of scalar fields in Robertson-Walker space-time

We study the lambda phi(4) field theory in a hat Robertson-Walker space-time using the functional Schrodinger picture. We introduce a simple Gaussian approximation to analyze the time evolution of pure states and we establish the renormalizability of the approximation. We also show that the energy-momentum tensor in this approximation is finite once we consider the usual mass and coupling constant renormalizations.