De Sitter Horizons & Holographic Liquids

TL;DR

This work builds a two-dimensional dilaton-gravity framework with solutions that interpolate from an $AdS_2$ boundary to a deep interior $dS_2$ horizon, enabling the use of boundary AdS/CFT tools to study de Sitter horizons. The authors derive the full boundary soft-mode action (a covariant Schwarzian) and analyse linear and nonlinear matter perturbations, including four-point functions, showing that the interpolating geometry yields oscillatory, not chaotic, OTOCs. They also examine Lorentzian shockwaves and Shapiro-type effects, highlighting sign-dependent time delays or advances tied to the bulk parameter $κ$ and the dilaton dynamics, and discuss implications for a holographic description of the de Sitter horizon. The results provide a concrete framework to model a putative holographic liquid for the de Sitter static patch and explore how interior geometry is reflected in boundary dynamics, with potential connections to dS/CFT and horizon microphysics.

Abstract

We explore asymptotically AdS$_2$ solutions of a particular two-dimensional dilaton-gravity theory. In the deep interior, these solutions flow to the cosmological horizon of dS$_2$. We calculate various matter perturbations at the linearised and non-linear level. We consider both Euclidean and Lorentzian perturbations. The results can be used to characterise the features of a putative dual quantum mechanics. The chaotic nature of the de Sitter horizon is assessed through the soft mode action at the AdS$_2$ boundary, as well as the behaviour of shockwave type solutions.

Figures (8)

• Figure 1: Penrose diagram for the interpolating solution. The dashed lines interpolate between a negative and a positive curvature region, that are coloured in light and darker blue, respectively. $\mathcal{C}$ is the boundary curve close to the AdS boundaries. Inside the horizons, the geometry is locally dS$_2$, but depending on whether $\kappa$ is positive or negative, the dilaton behaves as in the interior of a dS black hole or as in the dS cosmological patch.
• Figure 2: The perturbative solution for $m=-\phi_h=1$. (a) shows the full perturbative solution on the unit disk, while (b) zooms in the interpolating region. The unperturbed interpolating geometry is given by a separation between negative (blue) and positive (yellow) curvature at $\rho=0$ (dashed, red circle). The perturbation for $\kappa h_1^2 = 2.3$, generates the new curve with $\phi=0$ that is given by the black line in the plot. The black dashed line close to the boundary in Fig. (a) shows boundary conditions given by $\phi_b=30$, $h=900$.
• Figure 3: Perturbative solution with $m=-\phi_h=1$ on the unit disk. Yellow regions indicate positive curvature while blue ones, negative. The interpolating region with $\phi=0$ is the solid curve between them. The red dashed circle shows the interpolating region of the unperturbed geometry. As the strength of the perturbation increases, the positive curvature regions grow until negative curvature regions become disconnected.
• Figure 4: The propagator in equation (\ref{['propagator_global']}) as a function of $u$ is shown in green. In red, we plot the propagator for the perturbative Schwarzian action resulting near the boundary of the hyperbolic disk.
• Figure 5: Penrose diagrams for interpolating geometries after a shockwave perturbation.