# De Sitter Stability and Coarse Graining

## TL;DR

This paper analyzes the stability of de Sitter space using a coarse-grained approach that neglects horizon information, revealing that de Sitter space is unstable and evolves towards flat space with a thermodynamic interpretation.

## Contribution

It introduces a novel coarse-grained back reaction method for de Sitter space, showing its instability and proposing a thermodynamic perspective on the evolution.

## Key findings

- De Sitter space is unstable under coarse-grained back reaction.
- The Hubble rate evolves gradually and deviates from de Sitter at late times.
- The solutions suggest a dynamical vacuum energy decreasing over time.

## Abstract

We present a 4-dimensional back reaction analysis of de Sitter space for a conformally coupled scalar field in the presence of vacuum energy initialized in the Bunch-Davies vacuum. In contrast to the usual semi-classical prescription, as the source term in the Friedmann equations we use expectation values where the unobservable information hidden by the cosmological event horizon has been neglected i.e. coarse grained over. It is shown that in this approach the energy-momentum is precisely thermal with constant temperature despite the dilution from the expansion of space due to a flux of energy radiated from the horizon. This leads to a self-consistent solution for the Hubble rate, which is gradually evolving and at late times deviates significantly from de Sitter. Our results hence imply de Sitter space to be unstable in this prescription. The solution also suggests dynamical vacuum energy: the continuous flux of energy is balanced by the generation of negative vacuum energy, which accumulatively decreases the overall contribution. Finally, we show that our results admit a thermodynamic interpretation which provides a simple alternate derivation of the mechanism. For very long times the solutions coincide with flat space.