Disformal transformations as a change of units

TL;DR

Disformal transformations in inflationary theories are essentially changes of units, and this paper clarifies their role and implications, including effects on the tensor power spectrum and sound speed.

Contribution

The paper demonstrates that disformal transformations are equivalent to a change of units, clarifying their use in inflationary effective theories and resolving recent confusions.

Findings

Disformal transformations are equivalent to changing units.

Tensor power spectrum sensitivity to tensor sound speed.

Clarification of disformal transformations' role in perturbation theory.

Abstract

A disformal transformation is a very useful tool to analyze a general effective theory description of inflation. It can for example be used to set the tensor sound speed to unity, such that the tensor power spectrum only depends on the Hubble parameter. However, the disformal transformation has also led to quite some confusion in recent literature. We hope to clarify that confusion by pointing out that a disformal transformation is nothing else than a change of units. We show how everything that can be achieved by a (possibly time-dependent) disformal transformation, equally follows from the equivalent change of units, up to all orders in perturbation theory. We also comment on the sensitivity of the tensor power spectrum to a non-standard tensor speed of sound.