Effective interactions and prospects for a resolution of the fundamental cosmological problems in the quantum gravity

A possible effective interaction in the quantum gravity is considered. The compensation equation for a spontaneous generation of this interaction is shown to have a non-trivial solution. Would be consequences of a possible existence of effective interactions in the gravity theory are discussed. An example of running gravitational coupling is presented, which corresponds to a description of effects, which nowadays are prescribed to a dark mater and to a dark energy.