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, H₀ 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 H₀ = 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 10³, one assumes that any widespread field in the universe has a characteristic l₀ at the present epoch. Recent evidence from galaxy cluster RMs suggests that the largest reversal scale, l₀, 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).