  We introduce the relation between the holographic entropy bounds and the
inflationary universe. First the holographic entropy bounds for
radiation-dominated universe, radiation-dominated universe with a positive
cosmological constant are introduced. For an exact de Sitter phase, we use the
maximal entropy bound. We classify the inflation based on the quasi-de Sitter
spacetime into three steps: slow-roll period of inflation, epoch of reheating,
and radiation-dominated era. Then we study how to apply three entropy bounds to
the three steps of the inflation.
  Finally we discuss our results.
