Disformal invariance of curvature perturbation

Abstract

We show that under a general disformal transformation the linear comoving curvature perturbation is not identically invariant, but is invariant on superhorizon scales for any theory that is disformally related to Horndeski's theory. The difference between disformally related curvature perturbations is found to be given in terms of the comoving density perturbation associated with a single canonical scalar field. In General Relativity it is well-known that this quantity vanishes on superhorizon scales through the Poisson equation that is obtained on combining the Hamiltonian and momentum constraints, and we confirm that a similar result holds for any theory that is disformally related to Horndeski's scalar-tensor theory so long as the invertibility condition for the disformal transformation is satisfied. We also consider the curvature perturbation at full nonlinear order in the unitary gauge, and find that it is invariant under a general disformal transformation if we assume that an attractor regime has been reached. Finally, we also discuss the counting of degrees of freedom in theories disformally related to Horndeski's.

15 pages; Improved Sec. IV, added Appendix B and discussion on the invertibility of the disformal transformation in Sec. II; Improved discussion in Secs. II and IV, matches published version in JCAP

References in corpus (24)

• Covariant Galileon
• Healthy theories beyond Horndeski
• Avoiding Dark Energy with 1/R Modifications of Gravity
• Exploring gravitational theories beyond Horndeski
• A unifying description of dark energy
• Unifying framework for scalar-tensor theories of gravity
• Breaking of Vainshtein screening in scalar-tensor theories beyond Horndeski
• Disformal Transformations, Veiled General Relativity and Mimetic Gravity
• Third order equations of motion and the Ostrogradsky instability
• Astrophysical Probes of the Vainshtein Mechanism: Stars and Galaxies
• Hamiltonian analysis of spatially covariant gravity
• Derivative-dependent metric transformation and physical degrees of freedom
• Modified gravity inside astrophysical bodies
• Counting the degrees of freedom of generalized Galileons
• The two faces of mimetic Horndeski gravity: disformal transformations and Lagrange multiplier
• Hamiltonian structure of scalar-tensor theories beyond Horndeski
• Disformal transformation of cosmological perturbations
• Effective field theory approach to modified gravity including Horndeski theory and Hořava-Lifshitz gravity
• Shaken, not stirred: kinetic mixing in scalar-tensor theories of gravity
• Various Hamiltonian formulations of f(R) gravity and their canonical relationships
• Disformal invariance of cosmological perturbations in a generalized class of Horndeski theories
• Conservation of the nonlinear curvature perturbation in generic single-field inflation
• Observational signatures of the theories beyond Horndeski
• Multi-disformal invariance of nonlinear primordial perturbations

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