Infinite Temperature's Not So Hot

TL;DR

The paper introduces 'tomperature', a finite temperature-like parameter, to resolve the paradox of infinite temperature in de Sitter space's entanglement spectrum, demonstrated through a toy model involving SYK theory.

Contribution

It proposes and explains the concept of 'tomperature' to reconcile finite thermal behavior with a flat entanglement spectrum in de Sitter holography.

Findings

'Tomperature' remains finite as temperature approaches infinity.

Applied to the double-scaled SYK model, it resolves the de Sitter entropy puzzle.

Provides a new perspective on quantum thermal behavior in cosmological settings.

Abstract

It has been argued that the entanglement spectrum of a static patch of de Sitter space must be flat, or what is equivalent, the temperature parameter in the Boltzmann distribution must be infinite. This seems absurd: quantum fields in de Sitter space have thermal behavior with a finite temperature proportional to the inverse radius of the horizon. The resolution of this puzzle is that the behavior of some quantum systems can be characterized by a temperature-like quantity which remains finite as the temperature goes to infinity. For want of a better term we have called this quantity tomperature. In this paper we will explain how tomperature resolves the puzzle in a proposed toy model of de Sitter holography -- the double-scaled limit of SYK theory.