Multi-disformal invariance of nonlinear primordial perturbations

Abstract

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

8 pages

References in corpus (20)

• The Effective Field Theory of Inflation
• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• Improved Calculation of the Primordial Gravitational Wave Spectrum in the Standard Model
• Galileon inflation
• Non-Gaussianity in the modulated reheating scenario
• Multi-field galileons and higher co-dimension branes
• Unifying framework for scalar-tensor theories of gravity
• Primordial Curvature Fluctuation and Its Non-Gaussianity in Models with Modulated Reheating
• Resilience of the standard predictions for primordial tensor modes
• Multi-brid inflation and non-Gaussianity
• Primordial non-Gaussianity from the DBI Galileons
• Hamiltonian analysis of spatially covariant gravity
• Primordial non-Gaussianities in general modified gravitational models of inflation
• General Embedded Brane Effective Field Theories
• Large non-Gaussianity from multi-brid inflation
• On Classification of Models of Large Local-Type Non-Gaussianity
• Disformal transformation of cosmological perturbations
• Non-Gaussianity of superhorizon curvature perturbations beyond $\delta$ N formalism
• Non-Gaussian inflationary shapes in $G^3$ theories beyond Horndeski
• Full nonlinear growing and decaying modes of superhorizon curvature perturbations

Cited by in corpus (27)

• Derivative-dependent metric transformation and physical degrees of freedom
• Invariant quantities in the scalar-tensor theories of gravitation
• The two faces of mimetic Horndeski gravity: disformal transformations and Lagrange multiplier
• Relativistic stars in scalar-tensor theories with disformal coupling
• Cosmological disformal invariance
• General invertible transformation and physical degrees of freedom
• Invertible disformal transformations with higher derivatives
• Is there an effect of a nontrivial $c_T$ during inflation?
• Disformal invariance of curvature perturbation
• Invariant quantities in the multiscalar-tensor theories of gravitation
• Spatially covariant theories of gravity: disformal transformation, cosmological perturbations and the Einstein frame
• Conformal frames in cosmology
• Hybrid Higgs Inflation: The Use of Disformal Transformation
• Inflation with $R_{(\alpha \beta )}$ terms in the Palatini formulation
• New class of generalized coupling theories
• Cosmological disformal transformations to the Einstein frame and gravitational couplings with matter perturbations
• Disformal map and Petrov classification in modified gravity
• Vector disformal transformation of cosmological perturbations
• Gravitational Wave from Axion-SU(2) Gauge Fields: Effective Field Theory for Kinetically Driven Inflation
• Disformal invariance of cosmological observables
• Stars disformally coupled to a shift-symmetric scalar field
• Disformal transformation of physical quantities associated with relativistic stars
• Minimal exponential measure model in the post-Newtonian limit
• Scalar fields with derivative coupling to curvature in the Palatini and the metric formulation
• Cosmological attractors to general relativity and spontaneous scalarization with disformal coupling
• Derivative coupling of inflaton to $R^{(3)}$
• Disformal transformations as a change of units