Disformal transformation of cosmological perturbations

Abstract

We investigate the gauge-invariant cosmological perturbations in the gravity and matter frames in the general scalar-tensor theory where two frames are related by the disformal transformation. The gravity and matter frames are the extensions of the Einstein and Jordan frames in the scalar-tensor theory where two frames are related by the conformal transformation, respectively. First, it is shown that the curvature perturbation in the comoving gauge to the scalar field is disformally invariant as well as conformally invariant, which gives the predictions from the cosmological model where the scalar field is responsible both for inflation and cosmological perturbations. Second, in case that the disformally coupled matter sector also contributes to curvature perturbations, we derive the evolution equations of the curvature perturbation in the uniform matter energy density gauge from the energy (non)conservation in the matter sector, which are independent of the choice of the gravity sector. While in the matter frame the curvature perturbation in the uniform matter energy density gauge is conserved on superhorizon scales for the vanishing nonadiabatic pressure, in the gravity frame it is not conserved even if the nonadiabatic pressure vanishes. The formula relating two frames gives the amplitude of the curvature perturbation in the matter frame, once it is evaluated in the gravity frame.

15 pages

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Cited by in corpus (20)

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• Hairy black holes in DHOST theories: Exploring disformal transformation as a solution-generating method
• Invertible disformal transformations with higher derivatives
• Disformal invariance of cosmological perturbations in a generalized class of Horndeski theories
• Implications of Palatini gravity for inflation and beyond
• Generalized disformal Horndeski theories: cosmological perturbations and consistent matter coupling
• Inflation with $R_{(\alpha \beta )}$ terms in the Palatini formulation
• New class of generalized coupling theories
• Induced geometry from disformal transformation
• Inflationary gravitational waves in the effective field theory of modified gravity
• Non-Gaussianity in multi-sound-speed disformally coupled inflation
• Non-Gaussianity in DHOST inflation
• Generalized disformal invariance of cosmological perturbations with second-order field derivatives
• Scalar fields with derivative coupling to curvature in the Palatini and the metric formulation
• Potential-driven Inflation with Disformal Coupling to Gravity
• Extending the symmetry of the massless Klein-Gordon equation under the general disformal transformation
• On the KG-constrained general disformal transformation of the Einstein-Hilbert action
• Astro- and Quantum Physical Tests of Screened Scalar Fields