  It is widely believed that primordial magnetic fields are dramatically
diluted by the expansion of the universe. As a result, cosmological magnetic
fields with residual strengths of astrophysical relevance are generally sought
by going outside standard cosmology, or by extending conventional
electromagnetic theory. Nevertheless, the survival of strong B-fields of
primordial origin is possible in spatially open Friedmann universes without
changing conventional electromagnetism. The reason is the hyperbolic geometry
of these spacetimes, which slows down the adiabatic magnetic decay-rate and
leads to their superadiabatic amplification on large scales. So far, the effect
has been found to operate on Friedmannian backgrounds containing either
radiation or a slow-rolling scalar field. We show here that the superadiabatic
amplification of large-scale magnetic fields, generated by quantum fluctuations
during inflation, is essentially independent of the type of matter that fills
the universe and appears to be a generic feature of open Friedmann spacetimes.
We estimate the late-time strength of any residual field in a marginally open
universe and show that it can easily meet the requirements for the dynamo
generation of the magnetic fields observed in galaxies today.
