Conformal Symmetries of Adiabatic Modes in Cosmology

TL;DR

This paper reveals that scalar adiabatic perturbations in cosmology exhibit non-linearly realized conformal symmetries across various backgrounds, extending the understanding of symmetries beyond slow-roll scenarios.

Contribution

It demonstrates the presence of conformal symmetries in scalar perturbations for any cosmological background, including transformations beyond the standard dilatation.

Findings

Dilatation shifts curvature perturbation by a constant.

Scalar sector is invariant under special conformal transformations.

Tensor modes have their own non-linear symmetries and gauge transformations.

Abstract

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.