  We investigate possible astronomical manifestations of space-time anisotropy.
The homogeneous vacuum Kasner solution was chosen as a reference anisotropic
cosmological model because there are no effects caused by inhomogeneity in this
simple model with a constant degree of anisotropy. This anisotropy cannot
become weak. The study of its geodesic structure made it possible to clarify
the properties of this space-time. It showed that the degree of manifestation
of anisotropy varies significantly depending on the travel time of the light
from the observed object. For nearby objects, for which it does not exceed half
the age of the universe, the manifestations of anisotropy are very small.
Distant objects show more pronounced manifestations, for example, in the
distribution of objects over the sky and over photometric distances. These
effects for each of the individual objects decrease with time, but in general,
the manifestations of anisotropy in the Kasner space-time remain constant due
to the fact that new sources emerging from beyond the cosmological horizon.We
analyse observable signatures of the Kasner-type anisotropy and compare it to
observations. These effects were not found in astronomical observations,
including the study of the CMB. We can assume that the Universe has always been
isotropic or almost isotropic since the recombination era. This does not
exclude the possibility of its significant anisotropy at the moment of the Big
Bang followed by rapid isotropization during the inflationary epoch.
