Shape of the inflaton potential and the efficiency of the universe
  heating
  It is shown that the efficiency of the universe heating by an inflaton field
depends not only on the possible presence of parametric resonance in the
production of scalar particles but also strongly depends on the character of
the inflaton approach to its mechanical equilibrium point. In particular, when
the inflaton oscillations deviate from pure harmonic ones toward a succession
of step functions, the production probability rises by several orders of
magnitude. This in turn leads to a much higher temperature of the universe
after the inflaton decay, in comparison to the harmonic case. An example of the
inflaton potential is presented which creates a proper modification of the
evolution of the inflaton toward equilibrium and does not destroy the nice
features of inflation.
