# Cosmic equilibration: A holographic no-hair theorem from the generalized second law

## 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.

- Authors:

- California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics

- Publication Date:

- Research Org.:
- California Inst. of Technology (CalTech), Pasadena, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1422463

- Alternate Identifier(s):
- OSTI ID: 1501535

- Grant/Contract Number:
- SC0011632

- Resource Type:
- Journal Article: Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 97; Journal Issue: 4; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

### Citation Formats

```
Carroll, Sean M., and Chatwin-Davies, Aidan.
```*Cosmic equilibration: A holographic no-hair theorem from the generalized second law*. United States: N. p., 2018.
Web. doi:10.1103/physrevd.97.046012.

```
Carroll, Sean M., & Chatwin-Davies, Aidan.
```*Cosmic equilibration: A holographic no-hair theorem from the generalized second law*. United States. doi:10.1103/physrevd.97.046012.

```
Carroll, Sean M., and Chatwin-Davies, Aidan. Fri .
"Cosmic equilibration: A holographic no-hair theorem from the generalized second law". United States. doi:10.1103/physrevd.97.046012.
```

```
@article{osti_1422463,
```

title = {Cosmic equilibration: A holographic no-hair theorem from the generalized second law},

author = {Carroll, Sean M. and Chatwin-Davies, Aidan},

abstractNote = {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.},

doi = {10.1103/physrevd.97.046012},

journal = {Physical Review D},

issn = {2470-0010},

number = 4,

volume = 97,

place = {United States},

year = {2018},

month = {2}

}

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