Cosmological Observatories

TL;DR

This paper investigates the thermodynamic stability and linearized perturbations of the de Sitter static patch with conformal boundary conditions, revealing stability conditions and mode behaviors in various dimensions.

Contribution

It introduces a novel analysis of de Sitter space with conformal boundary conditions, exploring thermodynamic stability and mode structures, including quasinormal modes and fluid-like interpretations.

Findings

De Sitter space with conformal boundary conditions can be thermally stable depending on boundary extrinsic curvature.

In three dimensions, the spacetime is thermally stable for all constant boundary extrinsic curvature.

Linearized modes include quasinormal modes and fluid-like shear and sound modes, with some modes growing polynomially.

Abstract

We study the static patch of de Sitter space in the presence of a timelike boundary. We impose that the conformal class of the induced metric and the trace of the extrinsic curvature, $K$, are fixed at the boundary. We present the thermodynamic structure of de Sitter space subject to these boundary conditions, for static and spherically symmetric configurations to leading order in the semiclassical approximation. In three spacetime dimensions, and taking $K$ constant on a toroidal Euclidean boundary, we find that the spacetime is thermally stable for all $K$. In four spacetime dimensions, the thermal stability depends on the value of $K$. It is established that for sufficiently large $K$, the de Sitter static patch subject to conformal boundary conditions is thermally stable. This contrasts the Dirichlet problem for which the region encompassing the cosmological horizon has negative specific heat. We present an analysis of the linearised Einstein equations subject to conformal boundary conditions. In the worldline limit of the timelike boundary, the underlying modes are linked to the quasinormal modes of the static patch. In the limit where the timelike boundary approaches the cosmological event horizon, the linearised modes are interpreted in terms of the shear and sound modes of a fluid dynamical system. Additionally, we find modes with a frequency of positive imaginary part. Measured in a local inertial reference frame, and taking the stretched cosmological horizon limit, these modes grow at most polynomially.