Multi-disformal invariance of non-linear primordial perturbations

¹ Research Center for the Early Universe, University of Tokyo - Tokyo 113-0033, Japan
² Department of Physics, National Institute of Technology, Gunma College - Gunma 371-8530, Japan
³ Department of Physics, Tokyo Institute of Technology - Tokyo 152-8551, Japan
⁴ Yukawa Institute for Theoretical Physics, Kyoto University - Kyoto 606-8502, Japan

Received: 4 July 2015
Accepted: 23 July 2015

Abstract

We study disformal transformations of the metric in the cosmological context. We first consider the disformal transformation generated by a scalar field ϕ and show that the curvature and tensor perturbations on the uniform ϕ 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 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.