The origin of de Sitter entropy is more enigmatic than that of black holes. While the Gibbons–Hawking formula suggests a statistical interpretation, a concrete construction of the accessible microstates for a static-patch observer is still lacking. In this talk I present a systematic approach to this problem by constructing geometric microstates in two-dimensional flow (centaur) geometries that interpolate from an asymptotic AdS₂ boundary to a dS₂ static patch in the interior. Employing techniques from wormhole statistics and the gravitational path integral, we recover the expected area-law entropy and further show that the Hilbert space of the flow-geometry horizon is fully spanned by states whose time-symmetric slice contains a purely de Sitter Einstein–Rosen bridge with no residual AdS region. These controlled holographic states allow for an algebraic analysis of the information content of Hawking pairs. As a consequence of the Type II_∞ algebra, we derive a mini-Page curve whose behavior marks the moment at which quantum information begins to escape the cosmological horizon. Time permitting, I will also describe ongoing research into the scrambling algebra of a Hawking pair.

Biography

Dr. Ricardo Espíndola Romero obtained his PhD from the String Theory group at the University of Amsterdam in 2022. He has carried out research at various institutions, including the ICTP in Trieste, KU Leuven, the University of Southampton, the University of Barcelona, and UNAM in Mexico (where he was awarded the Alfonso Caso medal). He is currently a postdoctoral researcher at the Institute for Advanced Study at Tsinghua University, where he holds a Shuimu Tsinghua Scholarship. His main research focus is the holographic correspondence. The methods and concepts he has used in his research include entanglement entropy, wormhole physics, and von Neumann algebras.

Inviter: Jie-Qiang Wu