Seeing double: shock waves and the de Sitter horizon

TL;DR

This work analyzes how a displaced particle in de Sitter spacetime imparts time-dependent deformations to the cosmological horizon as it accelerates toward the horizon. By modeling the late-time, ultra-relativistic limit as a cosmological shock wave, the authors compute horizon distortions from slow-motion to shock-wave regimes using a static-patch holographic framework and observer-horizon construction. They find a parity-violating horizon shape at small velocities that becomes parity-preserving with two polar spikes in the shock-wave limit, signaling information transfer from the complementary static patch. The results support the view that the empty de Sitter horizon encodes data from all static patches, clarifying holographic implications and suggesting a Gauss’s-law–based interpretation via induced horizon stress tensors. Overall, the paper advances our understanding of horizon data encoding, information transfer across patches, and holographic descriptions of de Sitter spacetime.

Abstract

We consider a de Sitter observer in his rest frame at late times who observes a particle slightly displaced from unstable equilibrium. Initially, the observer notices an axisymmetric and parity-violating deformation along the trajectory of the displaced particle of his cosmological horizon. On a time scale of order $\ell$, the de Sitter radius, the particle is nearly absorbed by the cosmological horizon and has been accelerated to an ultra-relativistic speed and thus is well approximated as a shock wave. In the shock wave limit, the observer sees an axisymmetric deformation of his horizon with parity restored, which we interpret as arising due to a particle from the complementary static patch. We comment on the holographic implications of this result and note that there is no need to extend the holographic screen of de Sitter spacetime beyond the empty static patch to account for this signal.

Figures (6)

• Figure 1: The de Sitter hyperboloid embedding is shown with the $Z^2$ and $Z^3$ coordinates suppressed. The timelike world lines of two test particles in opposing static patches are shown in black as perturbations living on the empty de Sitter background.
• Figure 2: The de Sitter hyperboloid embedding is shown with the $Z^2$ and $Z^3$ coordinates suppressed. The world lines of two particles in opposing static patches that have been boosted are shown in black as perturbations living on the empty de Sitter background.
• Figure 3: In this Penrose diagram, a shock wave (shown in red) is along the $u$ axis. The observer is in the right patch. Due to the shock wave, the $u$ coordinate is shifted by $\Delta u=-\Theta (v) f(\theta)$. Effectively, the shock makes the diagram taller, and a signal from the left patch may come in to causal contact with the observer in the right patch.
• Figure 4: This is the horizon as seen by the observer when the particle is moving slowly and governed by eq \ref{['small_boost_horizon']}. The blue region near the North Pole shows the dip, while the yellowish region near the South Pole depicts the protrusion. In this case, the particle is moving along the $+ z$ axis and breaks parity. We plot the horizon using parameters $\ell=1000, \, m=100,\, T_o=2000,\,\tau=1,\, v=0.1$, which are outside the range of perturbative validity, to qualitatively illustrate the horizon's shape.
• Figure 5: The observer horizon due to the shock wave has two bumps on the north and south poles of the sphere. This is the horizon governed by \ref{['horizon deformed']} and shows that parity has been restored along the $z$ axis. In this plot, we use parameters $\ell=1000,\, T_o=1000 ,\, p=10$, which are outside the range of perturbative validity, to qualitatively show the horizon's shape.