We investigate a corner of the Bianchi models that has not received much attention : “ extended FLRW models ” ( eFLRW ) defined as a cosmological model with underlying anisotropic Bianchi geometry that nevertheless expands isotropically and can be mapped onto a reference FLRW model with the same expansion history .
In order to investigate the stability and naturalness of such models in a dynamical systems context , we consider spatially homogeneous models that contain a massless scalar field \varphi and a non-tilted perfect fluid obeying an equation of state p = w \rho .
Remarkably , we find that matter anisotropies and geometrical anisotropies tend to cancel out dynamically .
Hence , the expansion is asymptotically isotropic under rather general conditions .
Although extended FLRW models require a special matter sector with anisotropies that are “ fine-tuned ” relative to geometrical anisotropies , our analysis shows that such solutions are dynamically preferred attractors in general relativity .
Specifically , we prove that all locally rotationally symmetric Bianchi type III universes with space-like \nabla _ { \mu } \varphi are asymptotically shear-free , for all w \in [ -1 , 1 ] .
Moreover , all shear-free equilibrium sets with anisotropic spatial curvature are proved to be stable with respect to all homogeneous perturbations for w \geq - 1 / 3 .