Abstract
In this work, we study the effect of a magnetic field on the growth of cosmological perturbations. We develop a mathematical consistent treatment in which a perfect fluid and a uniform magnetic field evolve together in a Bianchi I universe. We then study the energy density perturbations on this background with particular emphasis on the effect of the background magnetic field. We develop a full relativistic solution which refines previous analysis in the relativistic limit, recovers the known ones in the Newtonian treatment with adiabatic sound speed, and it adds anisotropic effects to the relativistic ones for perturbations with wavelength within the Hubble horizon. This represents a refined approach on the perturbation theory of an isotropic universe in GR, since most of the present studies deal with fully isotropic systems.
Highlights
The formation of large scale structures across the Universe is one of the most fascinating and puzzling questions, still opened in theoretical cosmology
We develop a mathematical consistent treatment in which a perfect fluid and a uniform magnetic field evolve together in a Bianchi I universe
At the recombination the Universe Debye length is of the order of 10 cm and the implementation of a fluid theory, like general relativistic magneto-hydrodynamics is to be regarded as a valid and viable approach to treat the influence of the primordial magnetic field [7] on the evolution of perturbations [6]
Summary
The formation of large scale structures across the Universe is one of the most fascinating and puzzling questions, still opened in theoretical cosmology. General Relativistic Magneto-hydrodynamics formulation is an appropriate tool to investigate the impact of the Universe plasma features on structure formation, at least for a large range of the cosmological thermal history. In this context many works have been developed, mainly assuming as negligible the backreaction of the magnetic field on the isotropic Universe, see [19] and references therein. We recover the slowing-down of the growing mode in super-horizon scales, long known in FRW models This effect is very small given the upper limits on the cosmological magnetic fields, of order O v2A. The paper is structured as follows: in Sect. 3 we summarize the exact GRMHD equations in the 3+1 covariant formalism; in Sect. 4 we find the solution for the background Bianchi I model, we write the equations for the perturbations in synchronous gauge in Sect. 5 and we find the gauge modes in Sect. 6; we solve our system in some specific cases in Sect. 7 and we compare our results with present literature
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