Cosmological disformal invariance

TL;DR

This paper demonstrates that pure disformal transformations in gravity and matter theories do not alter physical observables, establishing their invariance at the action level and in cosmological perturbations, extending previous results and comparing with Horndeski theories.

Contribution

It proves that pure disformal transformations are physically invariant, equivalent to a time rescaling, and extends this invariance to cosmological perturbations and beyond Horndeski theories.

Findings

Disformal transformations are equivalent to time rescaling.

Physical observables remain invariant under disformal transformations.

Cosmological perturbations are invariant at linear and high orders.

Abstract

The invariance of physical observables under disformal transformations is considered. It is known that conformal transformations leave physical observables invariant. However, whether it is true for disformal transformations is still an open question. In this paper, it is shown that a pure disformal transformation without any conformal factor is equivalent to rescaling the time coordinate. Since this rescaling applies equally to all the physical quantities, physics must be invariant under a disformal transformation, that is, neither causal structure, propagation speed nor any other property of the fields are affected by a disformal transformation itself. This fact is presented at the action level for gravitational and matter fields and it is illustrated with some examples of observable quantities. We also find the physical invariance for cosmological perturbations at linear and high orders in perturbation, extending previous studies. Finally, a comparison with Horndeski and beyond Horndeski theories under a disformal transformation is made.