Rectifying an inconsistency in F(R) gravity inflation

Abstract

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 , frequently used in the literature, where 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 . 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.