**5.1. Searches for a magnetic field in the widespread
intergalactic medium up to the redshifts of quasars**

The availability of larger samples of extragalactic source rotation
measures in the 1970s led to the first tests for a Faraday rotation from
a widespread, and cosmologically scaled intergalactic magneto-ionic
medium
(Rees and Reinhardt
1972,
Nelson 1973,
Kronberg and
Simard-Normandin 1976).
The density,
*n*_{ig}(*z*), of a widespread intergalactic ionized gas
can be parameterized as a fraction,
of the total matter
density,
which increases with cosmological epoch as (1 + *z*)^{3}. For a
characteristic reversal scale of widespread IG magnetic field, a
measured RM (*z*) out to some maximum (*z*_{m}) can be
related to the widespread magnetic field using equation (1.3) modified
as follows:

(5.1) |

where

(5.2) |

for a
= 0 Friedmann
universe, *n*_{e} is in cm^{-3}, *c*
in km s^{-1}, *H*_{0} in km s^{-1}
Mpc^{-1}, and *B* in G.

If such a field were ordered on the scale of the universe, then an
observed systematic increase of RM(*z*) would occur for a preferred
direction in the sky which could, in principle also be determined
(Woltjer 1965,
Zel'dovich 1965,
Brecher and Blumenthal
1970).
Early claims to the detection of such an aligned field (e.g.
Sofue et al 1968) were
not substantiated in subsequent, better quasar RM data. These same data
limit any systematic growth of RM(*z*) to
5 rad m^{-2} or
less at *z* = 2.5
(Kronberg and Simard-Normandin 1976,
Kronberg 1976).
This, for a Friedmann universe with
= 1 and
*H*_{0} = 75
km s^{-1} Mpc^{-1}, places a limit on any
*cosmologically aligned* |*B*_{igm}| of
10^{-11}
G at the present epoch.

A field which is aligned on cosmological scales is unlikely. Given the
large scale homogeneity and isotropy of the universe back to the last
scattering surface at
*z* 10^{3},
one assumes that any widespread field in the universe has a
characteristic *l*_{0} at the present epoch. Recent
evidence from galaxy cluster RMs suggests that the largest reversal
scale, *l*_{0}, is crudely of order 1 Mpc. Scaling this by
(1 + *z*)^{-1} and applying the observational
limit to RM(*z*_{m}) out to
*z*_{m} = 2.5 gives |*B*_{igm}|
10^{-9} G
at the current epoch for any widespread, all-pervading field. With
future, more extensive and accurate RM data out
to larger *z*_{m} it should be possible to improve the
sensitivity of this measurement. 10^{-9} G lies at the upper end
of some recently calculated primordial field strengths generated in an
inflation cosmology (cf section 5.5 below).