The cosmological constant is causing the universe to expand at an accelerating rate. In the far future, when all matter has dispersed, only empty de Sitter space will remain — an ideal cosmic backdrop. But even in this emptiness, bounded by an event horizon, there is hidden life: quantum fluctuations give rise to a spectrum of states, like a faint hum.
The authors of the paper asked: what is the density of these states in the static patch of the three-dimensional de Sitter world? To answer, they constructed an intricate sum over a set of curved Kerr lens spaces. Each such space is associated with a line defect — the worldline of an observer sitting at the center of the static patch. The defect carries energy and spin, and its quantum description required invoking holographic duality.
The researchers applied the duality between gravity in three-dimensional de Sitter space and two copies of a complex Liouville string. In this dual picture, the Kerr lens spaces became generalized crosscap geometries. An exact calculation of string amplitudes on the crosscaps yielded a spectral density that matched the semiclassical approximation. For the simplest nontrivial case, the description reduced to two copies of an effective field theory of the double-scaled SYK model.
This approach places the physics of the horizon directly on the observer's worldline. Instead of trying to peer beyond the horizon, we obtain a hologram of the entire static patch in terms of the quantum mechanics of the observer-particle. This is a step toward a microscopic understanding of de Sitter entropy and, possibly, toward unraveling the nature of dark energy.
De Sitter space is the maximally symmetric solution to Einstein's equations with a positive cosmological constant. It is in such a universe that we will likely find ourselves billions of years from now, when accelerated expansion has finally pushed all galaxies beyond each other's horizons.
In Stanislaw Lem's novel "Fiasco," the protagonists encounter a civilization hidden behind an impenetrable event horizon — an attempt to make contact ends in catastrophe due to a misunderstanding of horizon physics.