Conformal Symmetries of Adiabatic Modes in Cosmology
  We remark on the existence of non-linearly realized conformal symmetries for
scalar adiabatic perturbations in cosmology. These conformal symmetries are
present for any cosmological background, beyond any slow-roll or quasi-de
Sitter approximation. The dilatation transformation shifts the curvature
perturbation by a constant, and corresponds to the well-known symmetry under
spatial rescaling. We argue that the scalar sector is also invariant under
special conformal transformations, which shift the curvature perturbation by a
term linear in the spatial coordinates. We discuss whether these conformal
symmetries can be extended to include tensor perturbations. Tensor modes
introduce their own set of non-linearly realized symmetries. We identify an
infinite set of large gauge transformations which maintain the transverse,
traceless gauge condition, while shifting the tensor mode non-trivially.
