Functional Schroedinger picture of a scalar field in a flat Robertson-Walker spacetime

The author studies free and self-interacting quantum field theories of a scalar field in the functional Schroedinger picture. He establishes the renormalizability of the Gaussian wavefunctional approximation to a time-dependent variational principle, both for the Minkowski and the flat Robertson-Walker spacetime. The renormalizability depends upon the specific initial state and reasonable criteria for limiting the initial conditions is discussed. For those initial states that satisfy these criteria, it is shown that the time-dependent variational equations, in the Minkowski spacetime, are made finite by the renormalization prescription used in the vacuum sector. In order to study the dynamics of spacetime in the early universe, he computes a finite and renormalized energy-momentum tensor for both the free and the interacting theory (in the Gaussian approximation) in Robertson-Walker spacetime. Using the adiabatic expansion, he shows that the entire subtraction necessary to make the energy-momentum tensor finite in the free theory can be written in terms of covariantly conserved tensors. He further shows that the same subtraction is sufficient to make the energy-momentum tensor finite in the Gaussian approximation for the interacting theory provided that the mass and the coupling constants are renormalized. As a demonstration of the usefulness of this formalism, the problem of the onset of inflation in the early universe is discussed and a sample numerical computation is presented