# Cosmic Equilibration: A Holographic No-Hair Theorem from the Generalized Second Law

## TL;DR

This paper proves a cosmic no-hair theorem linking entropy increase to the universe's evolution towards a de Sitter phase, using holographic and entropic principles without relying on Einstein's equations.

## Contribution

It establishes a new no-hair theorem based on generalized entropy and holographic screens, independent of Einstein's equations or a positive cosmological constant.

## Key findings

- Generalized entropy increases to a maximum in asymptotic de Sitter space
- The limiting entropy matches the de Sitter horizon entropy
- The proof does not depend on Einstein's field equations or a positive cosmological constant

## Abstract

In a wide class of cosmological models, a positive cosmological constant drives cosmological evolution toward an asymptotically de Sitter phase. Here we connect this behavior to the increase of entropy over time, based on the idea that de Sitter spacetime is a maximum-entropy state. We prove a cosmic no-hair theorem for Robertson-Walker and Bianchi I spacetimes that admit a Q-screen ("quantum" holographic screen) with certain entropic properties: If generalized entropy, in the sense of the cosmological version of the Generalized Second Law conjectured by Bousso and Engelhardt, increases up to a finite maximum value along the screen, then the spacetime is asymptotically de Sitter in the future. Moreover, the limiting value of generalized entropy coincides with the de Sitter horizon entropy. We do not use the Einstein field equations in our proof, nor do we assume the existence of a positive cosmological constant. As such, asymptotic relaxation to a de Sitter phase can, in a precise sense, be thought of as cosmological equilibration.