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We show that the difference between the theoretically expected and measuredby WMAP amplitude of the quadrupole fluctuations of CMB can be related to theimpact of the anisotropic curvature of the homogeneous universe dominated bythe dark energy. In such universe the matter expansion becomes practicallyisotropic just after the period of inflation and only at small redshifts theanisotropic expansion is generated again by the small curvature $\Omega_K=1-\Omega_m- \Omega_\Lambda \leq 10^{-4}$. For such models the possible deviationsfrom the parameters derived for the standard cosmological model are evidentlynegligible but the correlations of large scale perturbations and distortions oftheir Gaussianity are possible. Such models are also compatible with existenceof a homogeneous magnetic field and matter rotation which contribute to the low$\ell$ anisotropy and can be considered as ``hidden parameters'' of the model.Their influence can be observed as, for example, special correlations of smallscale fluctuations and the Faraday rotation of the CMB and radiation of thefarthest quasars. However, both the magnetic field and matter rotation requirealso modifications of the simple models of isotropic inflation and they changethe evolutionary history of the early Universe.Comment: 7 page

Extensions of the standard cosmological model: Anisotropy, rotation, and the magnetic field