Rectifying an Inconsistency in $F(R)$ Gravity Inflation
  In this letter we shall provide a formal derivation of the inflationary
slow-roll indices for $F(R)$ gravity from the power spectrum without the
condition $\dot{\epsilon}_1=0$, frequently used in the literature, where
$\epsilon_1=-\frac{\dot{H}}{H^2}$ is the first slow-roll index. We shall employ
Karamata's theorem for regularly varying functions, and as we show, we shall
derive the same expressions for the scalar and tensor spectral index of $F(R)$
gravity, also appearing in the current literature, without the misleading and
rather strong condition $\dot{\epsilon}_1=0$. The only conditions that are
needed are the slow-roll assumption, and the smallness of the slow-roll indices
and of their derivatives during inflation.
