  In this paper, we study the problem of massless particle creation in a flat,
homogeneous and isotropic universe in the framework of $f(G)$ gravity. The
Bogolyubov coefficients are calculated for the accelerating power-law solutions
of the model in a matter dominated universe, from which the total number of
created particle per unit volume of space can be obtained. It is proved that
the total particle density always has a finite value. Therefore, the Bogolyubov
transformations are well-defined and the Hilbert spaces spanned by the vacuum
states at different times are unitarily equivalent. We find that the particles
with small values of the mode $k$ are produced in the past and particles with
large values of $k$ are produced only in the future. The negative pressure
resulting from the gravitational particle creation is also determined. It is
then argued that this pressure even in the presence of energy density and
thermal pressure may affect significantly the cosmic expansion.
