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A few remarks on the relationship between elementary particle physics, gravitation and cosmology

We discuss some current problems in the relationship between elementary particle physics and gravitation, i.e., in the subject investigated by Prof.~K.~P.~Staniukovich half a century ago. Specifically, the inflationary stage of the Universe evolution, originating from the vacuum polarization and particle creation, corrections to Newton's gravitational law due to exchange of light elementary particles or spontaneous compactification of extra dimensions, and constraints on the parameters of axions as probable constituents of dark matter in our Universe are considered. It is pointed out that presently the relationship between elementary particles and gravitation has become an experimental science, and many experiments, directed towards resolution of all related problems, are performed in many countries.