Abstract
Primordial magnetic fields are often thought to be the early Universe seeds that have bloomed into what we observe today as galactic and extra-galactic magnetic fields. Owing to their minuscule strength, primordial magnetic fields are very hard to detect in cosmological and astrophysical observations. We show how this changes if a part of neutral Dark Matter has a magnetic susceptibility. In this way, by studying Dark Matter one can obtain information about the properties of primordial magnetic fields, even if the latter have a comoving amplitude B0 ≲ 0.01 nG. In our model Dark Matter is a stable singlet scalar χ, which interacts with electromagnetism through the Rayleigh operator as χ2FμνFμν/Λ2. For primordial magnetic fields present in the early Universe this operator forces the Z2-symmetry of the model to be spontaneously broken. Later, when the primordial magnetic field redshifts below a critical value, the symmetry is restored through an "inverse phase transition". At that point the field χ begins to oscillate and acts as a "magnetomorphic" Dark Matter component, inheriting the properties of the primordial magnetic field space distribution. In particular, for a nearly flat spectrum of magnetic field fluctuations, the scalar χ carries a statistically anisotropic isocurvature mode. We discuss the parameter space of the model and consider the possibility that the bulk of the Dark Matter is composed of the same particles χ produced via the freeze-in mechanism.