Conformal symmetries of adiabatic modes in cosmology

2012/03/28 by Kurt Hinterbichler, Lam Hui, Justin Khoury · 7 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Conformal geometry #Conformal gravity #Conformal map #Conformal symmetry #Cosmological perturbation theory #Cosmology #Cosmology and Gravitation Theories #Curvature #De Sitter universe #Galaxies: Formation, Evolution, Phenomena #Geometry #Homogeneous space #Mathematical physics #Physics #Quantum mechanics #Theoretical physics #astro-ph.CO #hep-th

paper · pdf · doi:10.1088/1475-7516/2012/08/017

published as JCAP 08(2012)017 · 16 pages

arxiv created 2012/03/28 · openalex publication_date 2012/08/17 · arxiv updated 2012/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems
• Conformal invariance of scalar perturbations in inflation
• Non-Gaussian correlations outside the horizon
• Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking
• Non-Gaussian features of primordial fluctuations in single field inflationary models
• Spontaneously Broken Spacetime Symmetries and Goldstone's Theorem
• Adiabatic modes in cosmology
• Spontaneous creation of almost scale-free density perturbations in an inflationary universe
• The dS/CFT correspondence
• The galileon as a local modification of gravity

Cited by

• The open effective field theory of inflation
• The separate universe approach to soft limits
• Asymptotic symmetries in de Sitter and inflationary spacetimes
• On the symmetries of cosmological perturbations
• Baryonic effects in the Effective Field Theory of Large-Scale Structure and an analytic recipe for lensing in CMB-S4
• The hemispherical asymmetry from a scale-dependent inflationary bispectrum
• Lagrangian space consistency relation for large scale structure