Is there supercurvature mode of massive vector field in open inflation?

Understand

We investigate the Euclidean vacuum mode functions of a massive vector field in a spatially open chart of de Sitter spacetime.

• In the one-bubble open inflationary scenario that naturally predicts a negative spatial curvature after a quantum tunneling, it is known that a light scalar field has the so-called supercurvature mode, i.e.
• an additional discrete mode which describes fluctuations over scales larger than the spatial curvature scale.
• If such supercurvature modes exist for a vector field with a sufficiently light mass, then they would decay slower and easily survive the inflationary era.