A microscopic model of de Sitter spacetime with an observer

TL;DR

This paper presents a microscopic quantum model of de Sitter spacetime with an observer, deriving entropy formulas and connecting them to the spectral density of the double scaled SYK model, offering insights into de Sitter holography.

Contribution

It introduces a simple microscopic model linking de Sitter entropy with the double scaled SYK model, providing a new holographic perspective.

Findings

Derived a formula for de Sitter entropy in a 3D Schwarzschild-de Sitter universe.

Matched the entropy formula with the spectral density of the double scaled SYK model.

Provided a de Sitter interpretation of two temperature notions in DSSYK.

Abstract

We introduce a simple microscopic quantum mechanical model of low-dimensional de Sitter holography with an observer. Using semiclassical gravity and elementary thermodynamic considerations, we derive a formula for the total entropy of a 3D Schwarzschild-de Sitter universe with an observer. We then match this entropy formula with the exactly known spectral density of the double scaled SYK model. Our result gives a de Sitter interpretation of the appearance of two notions of temperature in DSSYK.