# Four-volume cutoff measure of the multiverse

## Abstract

Predictions in an eternally inflating multiverse are meaningless unless we specify the probability measure. The scale-factor cutoff is perhaps the simplest and most successful measure which avoids catastrophic problems such as the youngness paradox, runaway problem, and Boltzmann brain problem, but it is not well defined in contracting regions with a negative cosmological constant. In this paper, we propose a new measure with properties similar to the scale-factor cutoff which is well-defined everywhere. The measure is defined by a cutoff in the four volume spanned by infinitesimal comoving neighborhoods in a congruence of timelike geodesics. The probability distributions for the cosmological constant and for the curvature parameter in this measure are similar to those for the scale-factor cutoff and are in a good agreement with observations.

- Authors:

- Publication Date:

- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

- Sponsoring Org.:
- National Science Foundation (NSF); Japan Society for the Promotion of Science (JSPS); USDOE Office of Science (SC), High Energy Physics (HEP)

- OSTI Identifier:
- 1599687

- Alternate Identifier(s):
- OSTI ID: 1802389

- Grant/Contract Number:
- SC0012567; PHY-1820872

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 101 Journal Issue: 4; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; Astronomy & Astrophysics; Physics

### Citation Formats

```
Vilenkin, Alexander, and Yamada, Masaki. Four-volume cutoff measure of the multiverse. United States: N. p., 2020.
Web. doi:10.1103/PhysRevD.101.043520.
```

```
Vilenkin, Alexander, & Yamada, Masaki. Four-volume cutoff measure of the multiverse. United States. https://doi.org/10.1103/PhysRevD.101.043520
```

```
Vilenkin, Alexander, and Yamada, Masaki. Fri .
"Four-volume cutoff measure of the multiverse". United States. https://doi.org/10.1103/PhysRevD.101.043520.
```

```
@article{osti_1599687,
```

title = {Four-volume cutoff measure of the multiverse},

author = {Vilenkin, Alexander and Yamada, Masaki},

abstractNote = {Predictions in an eternally inflating multiverse are meaningless unless we specify the probability measure. The scale-factor cutoff is perhaps the simplest and most successful measure which avoids catastrophic problems such as the youngness paradox, runaway problem, and Boltzmann brain problem, but it is not well defined in contracting regions with a negative cosmological constant. In this paper, we propose a new measure with properties similar to the scale-factor cutoff which is well-defined everywhere. The measure is defined by a cutoff in the four volume spanned by infinitesimal comoving neighborhoods in a congruence of timelike geodesics. The probability distributions for the cosmological constant and for the curvature parameter in this measure are similar to those for the scale-factor cutoff and are in a good agreement with observations.},

doi = {10.1103/PhysRevD.101.043520},

journal = {Physical Review D},

number = 4,

volume = 101,

place = {United States},

year = {2020},

month = {2}

}

https://doi.org/10.1103/PhysRevD.101.043520

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