00 1 Bianchi type IX world with torsion and shear

Oscillating phases in Bianchi type IX anisotropic universes are obtained as linearized solutions of Einstein-Cartan theory of gravity.Instead of making use of Weyssenhoff spinning fluids we addopt axionic torsion matter where the torsion tensor is totally skew-symmetric as in Kalb-Rammond type theories.Spin-torsion,metric and matter density oscillate at different phases. An upper bound oscillatory limit for torsion is obtained from the model. Metric coefficients correspond to two harmonic oscillators equations,the first describes a harmonic simple oscillator and the second a forced harmonic os-cillator. [2] have investigated in detail the Bianchi types I and V cosmological models in the realm of Einstein-Cartan theory of gravity [3]. In this letter a linearized solution of Einstein-Cartan (EC) theory representing a Bianchi type IX [4] cosmological model is presented.The solution possess the interesting feature of being an oscillating solution where the spin-torsion and matter densities oscillate at distinct phasess as well as the metric coefficients. Oscillating universes are important in the reheating phases of the Universe just after inflation. In fact this work in a certain sense is a continuation of our previous paper [4] on inflationary phases as a de Sitter solution of EC gravity.Anisotropic solutions could also lead to topological defects in EC gravity.The physical 1 motivation of using anisotropic models is according to Harko et al [1] be due to the fact that the spin is polarized. Since we only deal with linearized solution the structure of singularities on these models is out the scope of this work.Nevertheless is important to mention that the vacuum Bianchi type IX exact solution of Einstein field equation of General Relativity is already non-singular. Let us now consider the geometry of Bianchi type IX cosmological model is given by [5]