Entropy of de Sitter Spacetime: Analysis of Replica Wormholes

Abstract

Taking into account quantum effects, the cosmological horizon in de Sitter spacetime is seen to radiate by a static observer, just like the event horizon of the Schwarzschild black hole. A temperature and thermodynamic entropy is then associated to both. Regarding both universes as quantum systems, we can also consider the von Neumann entropy of their subregions. A side-by-side comparison between these spacetimes is made on their thermodynamic properties, quantum entropy and the application of replica wormholes to the von Neumann entropy of their radiation. For the black hole it is known a classical replica derivation of its von Neumann entropy results in exactly its thermodynamic entropy. We use the same method for the static patch in de Sitter spacetime and also find its thermodynamic entropy. Recently it was shown a semi-classical replica method can reproduce the island formula for radiation from an eternal black hole by including replica wormholes. Again, we apply the same calculation to de Sitter spacetime in the Bunch-Davies vacuum and recover the island formula.