  The specific astrophysical data collected during the last decade causes the
need for the modification of the expression for the Einstein-Hilbert action,
and several attempts sufficing this need are known. The modification suggested
in this paper stems from the possible anisotropy of space-time and this means
the natural change of the simplest scalar in the least action principle. To
provide the testable support to this idea, the optic-metrical parametric
resonance is regarded - an experiment on the galactic scale based on the
interaction between the electromagnetic radiation of cosmic masers and
periodical gravitational waves emitted by close double systems or pulsars.
Since the effect depends on the space-time metric, the possible anisotropy
could reveal itself through observations. To give the corresponding theory
predicting the corrections to the expected results of the experiment, the
specific mathematical formalism of Finsler geometry was chosen. It was found
that in case the anisotropy of the space-time exists, the orientation of the
astrophysical systems suitable for observations would show it. In the obtained
geodesics equation there is a direction dependent term.
