2015/04/02 by Yuki Watanabe, Atsushi Naruko, Misao Sasaki
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Classical mechanics #Context (archaeology) #Cosmology and Gravitation Theories #Curvature #Geometry #Invariant (physics) #Linear map #Mathematical physics #Mathematics #Physics #Pure mathematics #Scalar (mathematics) #Scalar field #Tensor (intrinsic definition) #Transformation (genetics) #astro-ph.CO #gr-qc #hep-th
paper · pdf · doi:10.1209/0295-5075/111/39002
8 pages
arxiv created 2015/04/02 · openalex publication_date 2015/08/01 · arxiv updated 2015/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.