Amplification of Primordial Gravitational Waves by a Geometrically
  Driven non-canonical Reheating Era
  In order to describe inflation in general relativity, scalar fields must
inevitably be used, with all the setbacks of that description. On the other
hand, $f(R)$ gravity and other modified gravity theories seem to provide a
unified description of early and late-time dynamics without resorting to scalar
or phantom theories. The question is, can modified gravity affect directly the
mysterious radiation domination era? Addressing this question is the focus in
this work, and we shall consider the case for which in the early stages of the
radiation domination era, namely during the reheating era, the background
equation of state parameter is different from $w=1/3$. As we show, in the
context of $f(R)$ gravity, an abnormal reheating era can affect the primordial
gravitational wave energy spectrum today. Since future interferometers will
exactly probe this era, which consists of subhorizon modes that reentered the
horizon during the early stages of the radiation domination era, the focus in
this work is how a short abnormal reheating era that deviates from the standard
perfect fluid pattern with $w\neq 1/3$, and generated by higher order curvature
terms, can affect the primordial gravitational wave energy spectrum. Using a
WKB approach, we calculate the effect of an $f(R)$ gravity generated abnormal
reheating era, and as we show the primordial gravitational wave spectrum is
significantly amplified, a result which is in contrast to the general
relativistic case, where the effect is minor.
