  In this work we shall consider the effects of a geometrically generated
post-inflationary era on the energy spectrum of the primordial gravitational
waves. Specifically, we shall consider a post-inflationary constant equation of
state era, generated by the synergistic effect of $f(R)$ gravity and of
radiation and matter perfect fluids. Two cases of interest shall be studied,
one with equation of state parameter $w=-1/3$, in which case the Universe
neither accelerates nor decelerates, and one with $w=0$ so an early matter
domination era. For the evaluation of the inflationary observational indices
which is relevant for the calculation of the gravitational waves energy
spectrum, we also took into account the effects of the constant equation of
state parameter era, on the $e$-foldings number. In both the $w=-1/3$ and $w=0$
cases, the energy spectrum of the primordial gravitational waves is amplified,
but for the $w=0$ case, the effect is stronger.
