  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.
