Mode spectrum of the electromagnetic field in open universe models

It has been claimed that in open FRW there exist magnetic field
modes which decay slower than at the usual "adiabatic" rate of
B ~ 1/a², so-called "supercurvature" modes. If they are present, it was
argued that the residual field strength in these modes could be of
cosmological relevance even if our Universe is only marginally open,
with (1 - Omega_0) << 1%. The question arises whether these speculated
supercurvature modes are actually part of the physical spectrum.

I begin with a review on the topic of supercurvature modes, which have
been studied in the scalar field context during the '90s. This will be
instructive in order to see under which conditions supercurvature modes
can arise, and an important result is that conformally coupled scalar
fields do not support supercurvature modes. It is therefore suggestive
that a similar result will also apply for conformally coupled vectors. A
detailed analysis of standard electromagnetism, very much along the
lines of the scalar field case, reveals that this is indeed the case. I
therefore conclude that, at least in the framework of open inflation,
the possible excitations of the electromagnetic field do not include any
supercurvature modes, and therefore the overall amplitude of the
magnetic field decays according to the standard "adiabatic" law.

Literature:
JA, Claudia de Rham, and Ruth Durrer, which has just shortly been
accepted for publication in MNRAS. arXiv: 1110.2019

Motivation for our work was: Barrow & Tsagas, MNRAS 414 (2011) 512
but see also earlier work quoted therein

Other relevant literature is rather old, the most relevant are:
Sasaki, Tanaka & Yamamoto, Phys. Rev. D51 (1995) 2979
Lyth & Woszczyna, Phys. Rev. D52 (1995) 3338
Garcia-Bellido, Garriga & Montes, Phys. Rev. D57 (1998) 4669
Mo & Papas, Phys. Rev. D6 (1972) 2071