A Bianchi Type IV Viscous Fluid Model of The Early Universe
  We are interested in formulating a viscous model of the universe based on The
Bianchi Type IV algebra. We first begin by considering a congruence of fluid
lines in spacetime, upon which, analyzing their propagation behaviour, we
derive the famous Raychaudhuri equation, but, in the context of viscous fluids.
We will then go through in great detail the topological and algebraic structure
of a Bianchi Type IV algebra, by which we will derive the corresponding
structure and constraint equations. From this, we will look at The Einstein
field equations in the context of orthonormal frames, and derive the resulting
dynamical equations: The \emph{Raychaudhuri Equation}, \emph{generalized
Friedmann equation}, \emph{shear propagation equations}, and a set of
non-trivial constraint equations. We show that for cases in which the bulk
viscous pressure is significantly larger than the shear viscosity, this
cosmological model isotropizes asymptotically to the present-day universe. We
finally conclude by discussing The Penrose-Hawking singularity theorem, and
show that the viscous universe under consideration necessarily emerged from a
past singularity point.
