Generalized disformal invariance of cosmological perturbations with second-order field derivatives
arXiv:2104.03662 · doi:10.1016/j.physletb.2021.136240
Abstract
We investigate how the comoving curvature and tensor perturbations are transformed under the generalized disformal transformation with the second-order covariant derivatives of the scalar field, where the free functions depend on the fundamental elements constructed with the covariant derivatives of the scalar field with at most the quadratic order of the second-order covariant derivatives. Our analysis reveals that on the superhorizon scales the difference between the comoving curvature perturbations in the original and new frames is given by the combination of the time derivative of the comoving curvature perturbation, the intrinsic entropy perturbation of the scalar field, and its time derivative in the original frame. Thus, in the case that on the superhorizon scales (1) the intrinsic entropy perturbation and its time derivative vanish and (2) the comoving curvature perturbation in the original frame, , is conserved, the comoving curvature perturbation becomes invariant under the disformal transformation on the superhorizon scales. We also show that the tensor perturbations are also disformally invariant, in the case that the tensor perturbations in the original frame are conserved with time.
11 pages, published version
References in corpus (10)
- The Standard Model Higgs boson as the inflaton
- Healthy theories beyond Horndeski
- G-inflation: inflation driven by the Galileon field
- Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order
- Vector Inflation
- Galileon inflation
- Breaking of Vainshtein screening in scalar-tensor theories beyond Horndeski
- Third order equations of motion and the Ostrogradsky instability
- Anisotropic Inflation from Vector Impurity
- Disformal transformation of cosmological perturbations