On the Scale of Inflation

TL;DR

The paper discusses the frame dependence of the inflation scale in cosmology, highlighting the challenges in defining it through observable quantities due to conformal transformations and inflaton-dependent couplings.

Contribution

It demonstrates that the inflationary scale cannot be fully characterized by tensor amplitude alone when couplings depend on the inflaton, emphasizing the importance of frame considerations.

Findings

Inflation scale is conformal frame dependent.

Tensor amplitude alone does not fully determine the inflationary scale.

Frame dependence complicates the interpretation of inflationary measurements.

Abstract

Because the scale of inflation is conformal frame dependent, in order to fully characterize it one should quote its value in terms of all the independent equal-time dimensionless ratios in the theory. We argue that when couplings depend on the inflaton itself, one cannot calculate these ratios in terms of measurable quantities such as the tensor amplitude and the Planck mass at present. This uncertainty also becomes manifest when we try to express the (frame-dependent) inflationary scale in terms of masses that are measurable today. Although we can calculate inflationary scale in the Einstein frame in terms of today's Planck mass, we cannot do the same in the Jordan frame. There are thus grounds to claim that the tensor amplitude does not completely characterize the scale of inflation.