Statistical Entropy of De Sitter Space

TL;DR

This paper adapts Carlip's black hole entropy approach to 2+1 dimensional quantum gravity with positive cosmological constant, deriving the statistical entropy of de Sitter space as proportional to its horizon area.

Contribution

It extends Carlip's method to de Sitter space in 2+1 dimensions, providing a statistical derivation of its entropy consistent with semiclassical predictions.

Findings

Statistical entropy matches quarter of the horizon area.

Entropy derivation aligns with semiclassical formulas.

Framework applies to quantum gravity with positive cosmological constant.

Abstract

Quantum gravity in 2+1 dimensions with a positive cosmological constant can be represented as an SL(2,C) Chern-Simons gauge theory. The symmetric vacuum of this theory is a degenerate configuration for which the gauge fields and spacetime metric vanish, while de Sitter space corresponds to a highly excited thermal state. Carlip's approach to black hole entropy can be adapted in this context to determine the statistical entropy of de Sitter space. We find that it equals one-quarter the area of the de Sitter horizon, in agreement with the semiclassical formula.