2021/10/05 by Jan de Boer, Jelle Hartong, de Boer, Jan +7 · 33 citations
Earth and Planetary Sciences · Physics and Astronomy · #Classical mechanics #Conformal map #Conformal symmetry #Cosmology #Cosmology and Gravitation Theories #Dark energy #De Sitter space #De Sitter universe #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometry #Geophysics and Gravity Measurements #High Energy Physics - Theory (hep-th) #Mathematical physics #Physics #Quantum mechanics #Scalar field #Solar and Space Plasma Dynamics #Symmetry (geometry) #Theoretical physics #Universe #gr-qc #hep-th
paper · pdf · open access · doi:10.48550/arxiv.2110.02319
published in Data Archiving and Networked Services (DANS) (Royal Netherlands Academy of Arts and Sciences) · 43 pages
arxiv created 2021/10/05 · openalex publication_date 2021/10/05 · arxiv updated 2021/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Carroll symmetry arises from Poincaré symmetry upon taking the limit of vanishing speed of light. We determine the constraints on the energy-momentum tensor implied by Carroll symmetry and show that for energy-momentum tensors of perfect fluid form, these imply an equation of state \cal E+P=0 for energy density plus pressure. Therefore Carroll symmetry might be relevant for dark energy and inflation. In the Carroll limit, the Hubble radius goes to zero and outside it recessional velocities are naturally large compared to the speed of light. The de Sitter group of isometries, after the limit, becomes the conformal group in Euclidean flat space. We also study the Carroll limit of chaotic inflation, and show that the scalar field is naturally driven to have an equation of state with w=-1. Finally we show that the freeze-out of scalar perturbations in the two point function at horizon crossing is a consequence of Carroll symmetry. To make the paper self-contained, we include a brief pedagogical review of Carroll symmetry, Carroll particles and Carroll field theories that contains some new material as well. In particular we show, using an expansion around speed of light going to zero, that for scalar and Maxwell type theories one can take two different Carroll limits at the level of the action. In the Maxwell case these correspond to the electric and magnetic limit. For point particles we show that there are two types of Carroll particles: those that cannot move in space and particles that cannot stand still.