  In this paper we present an exact solution to the spectrum of massless
particle creation for a power law expansion of the scale factor of the form
$t^{2n/3}$ for real scalar particles in a flat and matter dominated universe.
Such an evolution follows from a modified theory of gravity of the type
$f(R)=\beta R^n$, and it is showed that the spectrum of created particles is
$\beta$ independent. We find that greater the value of $n$ smaller is the
number of created particles. We study in detail the spectrum of the total
particle number created for $n=1\pm \varepsilon$, with $\varepsilon = 0.1$, a
very small deviation from the standard general relativity case ($n=1$). We find
that such a very small deviation causes a great difference in the total
particle number, of about one order of magnitude as compared to the standard
general relativity. Our calculations are based on the method of instantaneous
Hamiltonian diagonalization, where the vacuum states are defined as those which
minimizes the energy at a particular instant of time. The spectrum of the total
number and total energy of created particles can be determined exactly for any
value of the physical time in a matter dominated universe. We also find that
the main contribution to the total number of particles and total energy comes
from small wavenumbers $k$ and for particles with large values of $k$ the
contribution is very small.
