Possible extensions of the standard cosmological model: anisotropy, rotation, and magnetic field

We show that the difference between the theoretically expected and measured by WMAP amplitude of the quadrupole fluctuations of CMB can be related to the impact of the anisotropic curvature of the homogeneous universe dominated by the dark energy. In such universe the matter expansion becomes practically isotropic just after the period of inflation and only at small redshifts the anisotropic expansion is generated again by the small curvature $\Omega_K=1- \Omega_m- \Omega_\Lambda \leq 10^{-4}$. For such models the possible deviations from the parameters derived for the standard cosmological model are evidently negligible but the correlations of large scale perturbations and distortions of their Gaussianity are possible. Such models are also compatible with existence of 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 small scale fluctuations and the Faraday rotation of the CMB and radiation of the farthest quasars. However, both the magnetic field and matter rotation require also modifications of the simple models of isotropic inflation and they change the evolutionary history of the early Universe.