# Cosmological horizons, Noether charges and entropy

## TL;DR

This paper demonstrates that cosmological horizons, like black hole horizons, exhibit infinite-dimensional symmetries with associated conserved charges, which relate to horizon entropy and extend to various cosmological solutions.

## Contribution

It extends the concept of horizon symmetries and Noether charges from black holes to cosmological horizons, including de Sitter and black hole spacetimes, revealing their thermodynamic significance.

## Key findings

- Infinite-dimensional symmetry algebra at de Sitter horizon
- Noether charges are conserved, finite, and integrable
- Zero-mode charge accounts for Gibbons-Hawking entropy

## Abstract

It has recently been shown that, in the vicinity of their event horizons, black holes exhibit an infinite-dimensional symmetry. This symmetry captures relevant physical information about the black hole, and in particular about its thermodynamics. Here, we show that the same holds in a cosmological setup. More precisely, we show that around the de Sitter cosmological horizon, an infinite set of diffeomorphisms preserving a sensible set of boundary conditions emerges. These boundary conditions are similar to those considered by Price and Thorne in the context of the membrane paradigm, and permit to accommodate interesting gravity solutions. As for other boundary conditions considered previously, they are preserved by an infinite-dimensional asymptotic isometry algebra that includes supertranslations and two copies of the Virasoro algebra. This symmetry has associated a set of Noether charges that turn out to be conserved, finite, and integrable. We derive these charges explicitly using the covariant formalism and analyze their physical meaning by evaluating them to the case of de Sitter space. In this case, the zero-mode of the charge is found to account for the Gibbons-Hawking entropy of the cosmological horizon. We then consider a much more general set of solutions, including asymptotically de-Sitter black holes and asymptotically Taub-NUT-de Sitter black holes.