Natural vacuum state for quantum fields in an initially radiation dominated universe and its relationship to the Bunch-Davies state

It is shown that if the universe is initially radiation dominated, then for a scalar field with arbitrary mass and curvature coupling there is a natural vacuum state. The evolution of scalar fields in this vacuum state is investigated for a simple model where the presence of a cosmological constant causes the universe to expand exponentially at late times and thus to be asymptotically de Sitter. The question of whether the vacuum state approaches the Bunch-Davies state at late times is addressed.