Anisotropic cosmology and inflation from tilted Bianchi IX model

The dynamics of the tilted axisymmetric Bianchi IX cosmological models are explored allowing energy flux in the source fluid. The Einstein equations and the continuity equation are presented treating the equation of state $w$ and the tilt angle of the fluid $\lambda$ as time dependent functions, but when analysing the phase space $w$ and $\lambda$ are considered free parameters and the shear, the vorticity and the curvature of the spacetime span a three-dimensional phase space that contains seven fixed points. One of them is an attractor that inflates the universe anisotropically, thus providing a counter example to the cosmic no-hair conjecture. Also, examples of a realistic though fine-tuned cosmologies are presented wherein the rotation can grow significant towards the present epoch but the shear stays within the observational bounds. The examples suggest that the model used here can explain the parity-violating anomalies of the cosmic microwave background. The result significantly differs from an earlier study, where a non-axisymmetric Bianchi IX type with a tilted perfect dust source was found to induce too much shear for observationally significant vorticity.