Carroll symmetry, dark energy and inflation

TL;DR

The paper argues that Carroll symmetry, arising as the c→0 contraction of Poincaré, constrains the energy-momentum tensor so that for Carroll-invariant perfect fluids ${\cal E}+P=0$, linking the Carroll point to dark energy and inflation. It develops Carroll field theories (scalar and Maxwell) via a systematic small-c expansion and clarifies two distinct Carroll contractions (electric and magnetic) with explicit Lagrangians and EMTs. The authors then explore cosmological consequences: in the Carroll limit, the Friedmann dynamics favor an E+P=0 equation of state, producing de Sitter-like expansion, and chaotic inflation flows toward w = -1 with perturbations exhibiting horizon-crossing freeze-out due to Carroll symmetry. The work also reveals a holographic flavor, showing the de Sitter isometry group maps to Euclidean conformal symmetry in the Carroll limit, suggesting deeper connections between Carrollian physics and late-time cosmology.

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 ${\cal E}+P=0$ 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.

Figures (1)

• Figure 1: Consequences of a zero energy flux. Left: consider a particle with energy $E$ enclosed by a volume $V$. If the particle can move, it could leave $V$ and energy inside $V$ is not conserved unless $E=0$. If the particle cannot move, then there can be a non-zero rest energy $E_0$ which stays inside $V$. Particle decay of a particle with non-zero rest energy can also not happen. Right: interactions are possible, but only between particles of zero and non-zero energy, or between particles with zero energy. In this figure, particle 2 is attracted to particle 1, but to be consistent with zero-energy flux through $V_2$, it must have vanishing energy $E_2=0$. When it enters $V_1$, the total energy inside $V_1$ is then still conserved. Particle 1 is all the time at rest with rest energy $E_1$. Under Carroll boosts, energies stay the same, but velocities are rescaled.