  It is shown that the inflationary era in early universe is realized due to
the effect of backreaction of quantized matter fields. In fact we start by
quantizing a free scalar field in the Friedmann-Robertson-Walker space-time,
and the field is fluctuating quantum mechanically around the bottom of the mass
potential. We then obtain the vacuum expectation value of the energy density of
the scalar field as a functional of the scale factor $a(t)$ of the universe. By
plugging it into the Einstein equation, a self-consistent equation is
established in which the matter fields determine the time evolution of the
universe. We solve this equation by setting few conditions and find the
following solution: the universe expands \`{a} la de Sitter with e-folding
number $\gtrsim 60$ and then it turns to shrink with a decreasing Hubble
parameter $H(t)$ which rapidly goes to zero.
