Rectifying an inconsistency in F(R) gravity inflation

Department of Physics, Aristotle University of Thessaloniki - Thessaloniki 54124, Greece, Laboratory for Theoretical Cosmology, Tomsk State University of Control Systems and Radioelectronics (TUSUR) - 634050 Tomsk, Russia and Tomsk State Pedagogical University - 634061 Tomsk, Russia

Received: 17 March 2020
Accepted: 21 April 2020

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.