It has been claimed that in a Universe with open spatial geometry, despite their conformal invariance, magnetic fields do not need to decay as B~1/a2. The proposal is based on 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 a curvature scale many orders of magnitude larger than our Hubble radius.
Supercurvature modes have been studied in the scalar field context during the '90s. A review of this topic is instructive to see under which conditions they arise, and an important result states that conformally coupled scalar fields do not support supercurvature modes. It is suggestive that a similar result will also hold 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: Julian Adamek, Claudia de Rham, and Ruth Durrer, arXiv:1110.2019
Motivation for our work was: Barrow & Tsagas, MNRAS 414 (2011) 512, but see also earlier work quoted therein