Interpolating geometries and the stretched dS${}_2$ horizon

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.