We make use of a flat, axisymmetric Bianchi I metric to investigate the effects of a magnetic field upon the dynamics of the universe for the case in which the accompanying fluid is a cosmological constant and derive two exact solutions to the dynamical equations for this situation. We examine the behaviour of the scale factor perpendicular and parallel to the field lines, A(t) and W (t) respectively, and find the expected behaviour. The field has the strongest effect when A(t) is small, decelerating collapse perpendicular to the field lines, due to magnetic pressure, and accelerating collapse along the field lines, due to magnetic tension, while the vacuum energy dominates at late time, driving accelerated expansion.

If a magnetic field is frozen into a plasma that undergoes spherical compression, then the magnetic field B varies with the plasma density ρ according to B∝ρ2/3. In the gravitational collapse of cosmological density perturbations, however, quasi‐spherical evolution is very unlikely. In anisotropic collapses the magnetic field can be a much steeper function of gas density than in the isotropic case. We investigate the distribution of amplifications in realistic gravitational collapses from Gaussian initial fluctuations using the Zel'dovich approximation. Representing our results using a relation of the form B∝ρα, we show that the median value of α can be much larger than the value α= 2/3 resulting from spherical collapse, even if there is no initial correlation between magnetic field and principal collapse directions. These analytic arguments go some way towards understanding the results of numerical simulations.

We follow the growth of baryonic structure in the presence of a magnetic field within an approximate cosmological magnetohydrodynamic simulation, produced by adding an (isotropic) magnetic pressure related to the local gas pressure. We perform an ensemble of these simulations to follow the amplification of the field with time. By using a variety of initial field strengths and changing the slope of the power law that governs the way the field grows with increasing density, we span the range of current observations and demonstrate the size of the effect realistic magnetic fields could have on the central density of groups and clusters. A strong magnetic field significantly reduces the central gas density which, in turn, reduces observable quantities such as the X‐ray luminosity.

If a magnetic field is frozen into a plasma that undergoes spherical compression then the magnetic field B varies with the plasma density ρ according to B ∝ ρ 2/3 . In the gravitational collapse of cosmological density perturbations, however, quasi-spherical evolution is very unlikely. In anisotropic collapses the magnetic field can be a much steeper function of gas density than in the isotropic case. We investigate the distribution of amplifications in realistic gravitational collapses from Gaussian initial fluctuations using the Zel'dovich approximation. Representing our results using a relation of the form B ∝ ρ α , we show that the median value of α can be much larger than the α = 2/3 resulting from spherical collapse, even if there is no initial correlation between magnetic field and principal collapse directions. These analytic arguments go some way towards understanding the results of numerical simulations.

We follow the passive evolution of magnetic fields in SPH simulations to study their role in structure formation and galaxy clusters properties. Despite magnetic fields are not dynamically important for massive objects, they can still affect the properties of group-size objects and core regions and also affect particle's entropy.