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 ${\dot{\epsilon }}_1=0$, 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.

EPL Accepted

References in corpus (3)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• The Standard Model Higgs boson as the inflaton
• Inflationary Cosmology

Cited by in corpus (4)

• Inflationary Attractors in $F(R)$ Gravity
• Canonical Scalar Field Inflation with String and $R^2$-Corrections
• Power-Law $f(R)$ Gravity Corrected Canonical Scalar Field Inflation
• Kinetic Axion Dark Matter in String Corrected $f(R)$ Gravity