Transformation of Primordial Cosmological Perturbations Under the General Extended Disformal Transformation

Alinea, Allan L.; Kubota, Takahiro

doi:10.48550/arxiv.2005.12747

Cited by 4 publications

(8 citation statements)

References 57 publications

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“…where the nonzero difference arises from the disformal elements φ µν and g ρσ φ ρµ φ σν in Eq, ( 17), which were not discussed in Ref. [49]. This is because for instance the φ ij term in the spatial components of Eq.…”

Section: The Tensor Perturbationsmentioning

confidence: 97%

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Generalized disformal invariance of cosmological perturbations with second-order field derivatives

Minamitsuji

2021

Physics Letters B

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We investigate how the comoving curvature and tensor perturbations are transformed under the generalized disformal transformation with the second-order covariant derivatives of the scalar field, where the free functions depend on the fundamental elements constructed with the covariant derivatives of the scalar field with at most the quadratic order of the second-order covariant derivatives. Our analysis reveals that on the superhorizon scales the difference between the comoving curvature perturbations in the original and new frames is given by the combination of the time derivative of the comoving curvature perturbation, the intrinsic entropy perturbation of the scalar field, and its time derivative in the original frame. Thus, in the case that on the superhorizon scales (1) the intrinsic entropy perturbation and its time derivative vanish and (2) the comoving curvature perturbation in the original frame, Rc, is conserved, the comoving curvature perturbation becomes invariant under the disformal transformation on the superhorizon scales. We also show that the tensor perturbations are also disformally invariant, in the case that the tensor perturbations in the original frame are conserved with time.

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Section: The Tensor Perturbationsmentioning

confidence: 97%

“…On the other hand, Ref. [49] considered the disformal transformation with the secondorder covariant derivatives of the scalar field given by…”

Section: Introductionmentioning

confidence: 99%

Generalized disformal invariance of cosmological perturbations with second-order field derivatives

Minamitsuji

2021

Physics Letters B

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“…As we can see, this condition is clearly violated for non-zero E, therefore we arrive to the conclusion that the transformation (126) is not invertible unless E = 0. Once we generalize the structure of the higher-derivative term as [11,12]…”

Section: No-go For Disformal Transformation Of the Metric With Higher...mentioning

confidence: 99%

“…Let us consider the following generalization of the disformal transformation [11,12] gµν = F 0 g µν + F 1 χ µ χ ν + F 2 χ µν + F 3 χ (µ X ν) + F 4 X µ X ν + F 5 χ α µ χ να ,…”

Section: G1 Generalized Disformal Transformation With Second Derivativesmentioning

confidence: 99%

Invertibility conditions for field transformations with derivatives: toward extensions of disformal transformation with higher derivatives

Babichev,

Izumi,

Tanahashi

et al. 2021

Preprint

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We discuss a field transformation from fields ψ a to other fields φ i that involves derivatives, φ i = φi (ψ a , ∂ α ψ a , . . . ; x µ ), and derive conditions for this transformation to be invertible, primarily focusing on the simplest case that the transformation maps between a pair of two fields and involves up to their first derivatives. General field transformation of this type changes number of degrees of freedom, hence for the transformation to be invertible, it must satisfy certain degeneracy conditions so that additional degrees of freedom do not appear. Our derivation of necessary and sufficient conditions for invertible transformation is based on the method of characteristics, which is used to count the number of independent solutions of a given differential equation. As applications of the invertibility conditions, we show some non-trivial examples of the invertible field transformations with derivatives, and also give a rigorous proof that a simple extension of the disformal transformation involving a second derivative of the scalar field is not invertible.

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“…The symmetry of these perturbations are extended from conformal transformation to disformal transformation within the context of the Horndeski theory (see Refs. [17,18,19,20,21]). In the study of black holes in the context scalar tensor theories, disformal transformation can be used to investigate regions of the solution space and their symmetry [22].…”

Section: Introductionmentioning

confidence: 99%

On the Disformal Transformation of the Einstein-Hilbert Action

Alinea¹

2020

Preprint

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Disformal transformation is a generalisation of the well-known conformal transformation commonly elaborated in mainstream graduate texts in gravity (relativity) and modern cosmology. This transformation is one of the most important mathematical operations in scalar tensor theories attempting to address pressing problems involving dark energy and dark matter. With this topic yet to penetrate these texts, we present a pedagogically oriented derivation of the disformal transformation of the Einstein-Hilbert action. Along the way of calculation, we encounter apparently problematic terms that could be construed as leading to equations of motion that go beyond second order in derivatives, signalling instability. We demonstrate that these terms can be eliminated and absorbed through the definition of the Riemann curvature tensor. The transformed Einstein-Hilbert action turns out to be a special case of the Horndeski action and the equations of motion for the scalar field that it describes are all up to second order only in derivatives, implying stability.

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Transformation of Primordial Cosmological Perturbations Under the General Extended Disformal Transformation

Cited by 4 publications

References 57 publications

Generalized disformal invariance of cosmological perturbations with second-order field derivatives

Generalized disformal invariance of cosmological perturbations with second-order field derivatives

Invertibility conditions for field transformations with derivatives: toward extensions of disformal transformation with higher derivatives

On the Disformal Transformation of the Einstein-Hilbert Action

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