Multi-disformal invariance of nonlinear primordial perturbations

TL;DR

This paper investigates the invariance of nonlinear primordial perturbations under disformal transformations, including a new multi-component scalar field transformation, revealing conditions for invariance at various orders.

Contribution

It introduces the concept of multi-disformal transformations and demonstrates their invariance properties for curvature and tensor perturbations at linear and nonlinear levels.

Findings

Curvature and tensor perturbations are non-linearly invariant under scalar-field disformal transformations.

The invariance extends to multi-disformal transformations with multi-component scalar fields in the adiabatic limit.

Different descriptions of the transformation highlight physical invariance versus apparent causal structure changes.

Abstract

We study disformal transformations of the metric in the cosmological context. We first consider the disformal transformation generated by a scalar field $\phi$ and show that the curvature and tensor perturbations on the uniform $\phi$ slicing, on which the scalar field is homogeneous, are non-linearly invariant under the disformal transformation. Then we discuss the transformation properties of the evolution equations for the curvature and tensor perturbations at full non-linear order in the context of spatial gradient expansion as well as at linear order. In particular, we show that the transformation can be described in two typically different ways: one that clearly shows the physical invariance and the other that shows an apparent change of the causal structure. Finally we consider a new type of disformal transformation in which a multi-component scalar field comes into play, which we call a "multi-disformal transformation". We show that the curvature and tensor perturbations are invariant at linear order, and also at non-linear order provided that the system has reached the adiabatic limit.