Primordial Magnetic Fields and Causality

We discuss the implications of causality on a primordial magnetic field. We show that the residual field on large scales is much more suppressed than usually assumed and that a helical component is even more reduced. Due to this strong suppression, even maximal primordial fields generated at the electroweak phase transition can just marginally seed the fields in clusters, but they cannot leave any detectable imprint on the cosmic microwave background.