SHEAR-FREE, IRROTATIONAL, GEODESIC, ANISOTROPIC FLUID COSMOLOGIES

General relativistic anisotropic fluid models whose fluid flow lines f orm a shear-free, irrotational, geodesic timelike congruence are exami ned. These models are of Petrov type D, and are assumed to have zero h eat flux and an anisotropic stress tensor that possesses two distinct non-zero eigenvalues. Some general results concerning the form of the metric and the stress tensor for these models are established. Further more, if the energy density and the isotropic pressure, as measured by a co-moving observer, satisfy an equation of state of the form p = p( mu), with dp/dmu not-equal -1/3, then these spacetimes admit a foliati on by spacelike hypersurfaces of constant Ricci scalar. In addition, m odels for which both the energy density and the anisotropic pressures only depend on time are investigated; both spatially homogeneous and s patially inhomogeneous models are found. A classification of these mod els is undertaken. Also, a particular class of anisotropic fluid model s which are simple generalizations of the homogeneous isotropic cosmol ogical models is studied.