  It is known that the unregularized expressions for the stress-energy tensor
components corresponding to subhorizon and superhorizon vacuum fluctuations of
a massless scalar field in a Friedmann-Robertson-Walker background are
characterized by the equation of state parameters w=1/3 and w=-1/3, which are
not sufficient to produce cosmological acceleration. However, the form of the
adiabatically regularized finite stress-energy tensor turns out to be
completely different. By using the fact that vacuum subhorizon modes evolve
nearly adiabatically and superhorizon modes have w=-1/3, we approximately
determine the regularized stress-energy tensor, whose conservation is utilized
to fix the time dependence of the vacuum energy density. We then show that
vacuum energy density grows from zero up to H^4 in about one Hubble time,
vacuum fluctuations give positive acceleration of the order of H^4/M_p^2 and
they can completely alter the cosmic evolution of the universe dominated
otherwise by cosmological constant, radiation or pressureless dust. Although
the magnitude of the acceleration is tiny to explain the observed value today,
our findings indicate that the cosmological backreaction of vacuum fluctuations
must be taken into account in early stages of cosmic evolution.
