Interpolating geometries and the stretched dS$_2$ horizon

TL;DR

This paper explores dilaton-gravity models with dS$_2$ regions, analyzing their thermodynamics, phase transitions, and the potential for near-AdS$_2$ boundaries to serve as completions of the stretched dS$_2$ horizon.

Contribution

It introduces new insights into the thermodynamic stability and phase structure of dilaton-gravity models with dS$_2$ geometries, including the role of near-AdS$_2$ boundaries.

Findings

Certain geometries are thermodynamically stable at specific temperatures.

First order phase transitions similar to Hawking-Page are identified.

Near-AdS$_2$ boundaries can complete the stretched dS$_2$ horizon.

Abstract

We investigate dilaton-gravity models whose solutions contain a large portion of the static patch of dS$_2$. The thermodynamic properties of these theories are considered both in the presence of a finite Dirichlet wall, as well as for asymptotically near-AdS$_2$ boundaries. We show that under certain circumstances such geometries, including those endowed with an asymptotically near-AdS$_2$ boundary, can be locally and even globally thermodynamically stable within particular temperature regimes. First order phase transitions reminiscent of the Hawking-Page transition are discussed. For judiciously chosen models, the near-AdS$_2$ boundary can be viewed as a completion of the stretched cosmological dS$_2$ horizon. We speculate on candidate microphysical models.