Understand
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.