On the Scale of Inflation

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.