Cosmological model with perfect fluid and de Sitter universe

Shear-free cosmological models are too simple for cosmological purposes and they contain all the classical FLRW cosmological models, also with pressure. They are capable of reproducing the classical cosmological results in the limit. The cosmiological model based on the shear-free spherically symmetric solution of Einstein’s equations for the perfect fluid with uniform density but with nonuniform pressure is very attractive for many reasons. Special interest is the fact, that for the homogeneous anisotropic perfect fluid exist common solution, which containe three types of spaces as special cases. The spatial curvature and other invariants of the curvature tensor of the homogeneous anisotropic perfect fluid depends on time only by the function £(i). This solutions also extremely close to the FLRW solutions. The composite cosmological model has been built. The de Sitter solution and shear-free solution of perfect fluid are fitting on the hypersurface r = const. The Lichnerowicz-Darmois matching conditions are used. It was found, that energy density of considered model on the boundary equals to the energy density of the de Sitter’s solution, i.e. this cosmological model has no initial singularity.