Is there supercurvature mode of massive vector field in openinflation?

Abstract

We investigate the Euclidean vacuum mode functions of a massive vectorfield in a spatially open chart of de Sitter spacetime. In theone-bubble open inflationary scenario that naturally predicts a negative spatial curvature after a quantum tunneling, it is known that a lightscalar field has the so-called supercurvature mode, i.e. an additionaldiscrete mode which describes fluctuations over scales larger than thespatial curvature scale. If such supercurvature modes exist for a vectorfield with a sufficiently light mass, then they would decay slower and easily survive the inflationary era. However, the existence ofsupercurvature mode strongly depends on details of the system. Toclarify whether a massive vector field has supercurvature modes, weconsider a U(1) gauge field with gauge and conformal invariances spontaneously broken through the Higgs mechanism, and present explicit expressions for the Euclidean vacuum mode functions. We findthat, for any values of the vector field mass, there is nosupercurvature mode. In the massless limit, the absence ofsupercurvature modes in the scalar sector stems from the gaugesymmetry.