Cosmological disformal invariance

Abstract

The invariance of physical observables under disformal transformations is considered. It is known that conformal transformations leave physical observables invariant. However, whether it is true for disformal transformations is still an open question. In this paper, it is shown that a pure disformal transformation without any conformal factor is equivalent to rescaling the time coordinate. Since this rescaling applies equally to all the physical quantities, physics must be invariant under a disformal transformation, that is, neither causal structure, propagation speed nor any other property of the fields are affected by a disformal transformation itself. This fact is presented at the action level for gravitational and matter fields and it is illustrated with some examples of observable quantities. We also find the physical invariance for cosmological perturbations at linear and high orders in perturbation, extending previous studies. Finally, a comparison with Horndeski and beyond Horndeski theories under a disformal transformation is made.

23 pages + Appendix, updated version

References in corpus (29)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe
• Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase
• Healthy theories beyond Horndeski
• Exploring gravitational theories beyond Horndeski
• Phantom scalar dark energy as modified gravity: understanding the origin of the Big Rip singularity
• Model independent evidence for dark energy evolution from Baryon Acoustic Oscillations
• The (pseudo)issue of the conformal frame revisited
• Cosmology with Mimetic Matter
• A unifying description of dark energy
• Screening Modifications of Gravity through Disformally Coupled Fields
• Unifying framework for scalar-tensor theories of gravity
• Resilience of the standard predictions for primordial tensor modes
• Einstein and Jordan frames reconciled: a frame-invariant approach to scalar-tensor cosmology
• Disformal Transformations, Veiled General Relativity and Mimetic Gravity
• Effective Theory of Interacting Dark Energy
• Invariant quantities in the scalar-tensor theories of gravitation
• Disformal couplings and the dark sector of the universe
• Disformal Theories of Gravity: From the Solar System to Cosmology
• Constraining Disformally Coupled Scalar Fields
• Conformal Frame Dependence of Inflation
• Disformal transformation of cosmological perturbations
• Towards Viable Cosmological Models of Disformal Theories of Gravity
• Shaken, not stirred: kinetic mixing in scalar-tensor theories of gravity
• Note on Varying Speed of Light Cosmologies
• Disformal invariance of cosmological perturbations in a generalized class of Horndeski theories
• Multi-disformal invariance of nonlinear primordial perturbations
• Disformal quintessence
• Explaining the Proton Radius Puzzle with Disformal Scalars

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