The cosmological model with an analytic exit from inflation

A cosmological model of homogeneous and isotropic spatially flat Universe with gravitating self-interacting scalar field is considered. The exact solution, admitting an analytical exit from inflationary stage into a radiation era and a matter dominated epoch, is obtained by virtue of ``fine turning of the potential'' method. We found that an inflationary stage is supported by decay of higgs bosons in the framework of the solution obtained. Freidmann's regim is associated with adiabatical expantion of the Universe, filled by the matter with special equation of state. Thus we presented the exact solution which solve the problem of transition from an inflationary to a radiation eras or long standing `exit' problem.