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

We study the $λϕ^4$ field theory in a flat Robertson-Walker space-time using the functional Schödinger 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.

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