A large scale coherent magnetic field: interactions with free streaming particles and limits from the CMB

Abstract

We study a homogeneous and nearly-isotropic Universe permeated by a homogeneous magnetic field. Together with an isotropic fluid, the homogeneous magnetic field, which is the primary source of anisotropy, leads to a plane-symmetric Bianchi I model of the Universe. However, when free-streaming relativistic particles are present, they generate an anisotropic pressure which counteracts the one from the magnetic field such that the Universe becomes isotropized. We show that due to this effect, the CMB temperature anisotropy from a homogeneous magnetic field is significantly suppressed if the the neutrino masses are smaller than 0.3 eV.

A non-perturbative study of the evolution of cosmic magnetised sources

“…In other words: a magnetised Bianchi I model that becomes arbitrarily close to its FLRW particular case (by considering sufficiently weak magnetic fields) may only describe approximately an exact perturbation of a unique scale of infinite spatial extent, and as such can approximate only very large scale supra-horizon perturbations as, for example, in various string inspired inflationary magnetogenesis scenarios (see details in [8,9,10,11] and also in [26]), and in the Bianchi I model used in [37] to study for the interaction of free streaming neutrinos and such large scale weak magnetic field.…”

“…Work along these lines is found in older literature (see pioneering work in [31]) considering very simple highly idealised fluids (even dust) in solutions with cylindrical symmetry [32], or homogeneous but anisotropic Bianchi models [33] and, in particular, spatially flat Bianchi I models [34,35,36], which provide the simplest spacetime geometry compatible with the anisotropic stresses that characterise the magnetic interaction. More recently [37], a Bianchi I model was used to examine how the anisotropic stresses produced by free streaming neutrinos (described in terms of relativistic Kinetic Theory) allow for the fulfilment of the late time constraints placed by the CMB on the anisotropy of large scale (supra-horizon) magnetic fields 1 .…”

“…Instead of considering idealised fluids whose interaction with the magnetic field is unspecified (as in [32,33,34,35,36]), or a collision-less kinetic theory approach (suited to free streaming collision-less conditions as in [37]), we consider fluid sources that satisfy physically motivated equations of state that are well suited for an early Universe cosmic fluid interacting with a magnetic field within a hydrodynamical regime, namely: a mixture of ideal gasses of magnetised fermions [39,40,41] whose equation of state reflects the full anisotropic effects of the magnetic field. Evidently, this field introduces anisotropic momentum fluxes that modify the energy-momentum tensor and thus affect the evolution of the state variables.…”

“…These bounds were obtained without considering the anisotropy introduced by the magnetic field. On the other hand, fitting CMB observations leads to a stronger constraint that appears to exclude homogeneous cosmological magnetic fields much stronger than 10 −9 G [9,37].…”

“…This comparison is facilitated by our choice of a Bianchi I model that becomes a spatially flat FLRW model when the magnetic field vanishes (i.e. the magnetic field is the sole cause of anisotropy of the source), as in this case a sufficiently weak field can be regarded approximately as a sort of supra-horizon magnetic perturbation on a spatially flat FLRW background (see comments on this issue in [37]), but it lends naturally with a comparison in the weak field regime studied in [25,26,30] and in [8]. Without neglecting the importance of observational bounds, the obtained results may be useful in potential situations in which strong cosmic magnetic field need to be examined in a non-perturbative manner.…”