Dynamics of a magnetized Bianchi I universe with vacuum energy

Abstract

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.

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

“…an FLRW geometry), as the energy-momentum tensor (36) can still be compatible with the inherent anisotropy of the Bianchi I geometry that is present in the different fluid expansion rates in (50) and the nonzero shear tensor in (51) and (52) (see Appendix A). Hence, a zero magnetic field in a Bianchi I model only leads to an FLRW geometry if besides the magnetic field the shear tensor vanishes as well.…”

“…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.…”

Dynamics of a self-gravitating neutron source

“…It is possible to introduce a temperature dependence in the equation of state. Buy doing so, the of evolution of the neutron gas could be associated with high temperature neutron sources in the context of early universe conditions in cosmological models dealing with primordial magnetic field [22].…”

Untitled

“…To discuss the effects of magnetic flux on the evolution of the Universe, King & Coles [27] used the magnetic perfect fluid energy-momentum tensor. Bianchi type-I cosmological model in the presence of magnetic anisotropic dark energy is obtained by Sharif & Zubair [28].…”