## Abstract

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 (Formula presented.) 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.

Original language | English |
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Article number | 810405 |

Journal | Frontiers in Physics |

Volume | 10 |

DOIs | |

Publication status | Published - 8 Apr 2022 |

### Bibliographical note

Funding Information:JB is supported by the European Research Council under the European Unions Seventh Framework Programme (FP7/2007-2013), ERC Grant agreement ADG 834878. JH is supported by the Royal Society University Research Fellowship ``Non-Lorentzian Geometry in Holography'' (Grant Number UF160197). NO is supported in part by the project ``Towards a deeper understanding of black holes with non-relativistic holography'' of the Independent Research Fund Denmark (grant number DFF-6108-00340) and by the Villum Foundation Experiment project 00023086. WS is supported by the Icelandic Research Fund (IRF) via a Personal Postdoctoral Fellowship Grant (185371-051).

Publisher Copyright:

Copyright © 2022 de Boer, Hartong, Obers, Sybesma and Vandoren.

## Other keywords

- carroll symmetry
- carrollian dynamics
- dark energy
- field theory
- inflation