  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.
