The Casimir energy of a degenerate double well

The true Casimir energy of a scalar field in a degenerate double well potential is shown to be reduced in comparison to the Casimir energy of a free field oscillating in one of the bare vacua due to tunneling effects. The cases of massive and massless scalar fields are analyzed, where symmetry breaking is triggered by a negative mass squared term and a negative scalar-curvature coupling respectively. In the latter case, the energy reduction is enough to change the sign of the Casimir energy, and potential applications to early universe cosmology are discussed.