## Inhomogeneous anisotropic cosmology

## Abstract

In homogeneous and isotropic Friedmann-Robertson-Walker cosmology, the topology of the universe determines its ultimate fate. If the Weak Energy Condition is satisfied, open and flat universes must expand forever, while closed cosmologies can recollapse to a Big Crunch. A similar statement holds for homogeneous but anisotropic (Bianchi) universes. Here in this paper, we prove that arbitrarily inhomogeneous and anisotropic cosmologies with "flat'' (including toroidal) and "open'' (including compact hyperbolic) spatial topology that are initially expanding must continue to expand forever at least in some region at a rate bounded from below by a positive number, despite the presence of arbitrarily large density fluctuations and/or the formation of black holes. Because the set of 3-manifold topologies is countable, a single integer determines the ultimate fate of the universe, and, in a specific sense, most 3-manifolds are "flat" or "open". Our result has important implications for inflation: if there is a positive cosmological constant (or suitable inflationary potential) and initial conditions for the inflaton, cosmologies with "flat'' or "open" topology must expand forever in some region at least as fast as de Sitter space, and are therefore very likely to begin inflationary expansion eventually, regardless of the scale of the inflationary energymore »

- Authors:

- New York Univ. (NYU), NY (United States). Center for Cosmology and Particle Physics
- Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics and Dept. of Physics; SLAC National Accelerator Lab., Menlo Park, CA (United States). Kavli Inst. for Particle Astrophysics and Cosmology

- Publication Date:

- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States); Stanford Univ., CA (United States)

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

- OSTI Identifier:
- 1353055

- Alternate Identifier(s):
- OSTI ID: 1491173

- Grant/Contract Number:
- AC02-76SF00515; PHY-1214302; SC0008078

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Cosmology and Astroparticle Physics

- Additional Journal Information:
- Journal Volume: 2016; Journal Issue: 10; Journal ID: ISSN 1475-7516

- Publisher:
- Institute of Physics (IOP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; gravity; initial conditions and eternal universe; cosmological simulations; inflation

### Citation Formats

```
Kleban, Matthew, and Senatore, Leonardo. Inhomogeneous anisotropic cosmology. United States: N. p., 2016.
Web. doi:10.1088/1475-7516/2016/10/022.
```

```
Kleban, Matthew, & Senatore, Leonardo. Inhomogeneous anisotropic cosmology. United States. doi:10.1088/1475-7516/2016/10/022.
```

```
Kleban, Matthew, and Senatore, Leonardo. Wed .
"Inhomogeneous anisotropic cosmology". United States. doi:10.1088/1475-7516/2016/10/022. https://www.osti.gov/servlets/purl/1353055.
```

```
@article{osti_1353055,
```

title = {Inhomogeneous anisotropic cosmology},

author = {Kleban, Matthew and Senatore, Leonardo},

abstractNote = {In homogeneous and isotropic Friedmann-Robertson-Walker cosmology, the topology of the universe determines its ultimate fate. If the Weak Energy Condition is satisfied, open and flat universes must expand forever, while closed cosmologies can recollapse to a Big Crunch. A similar statement holds for homogeneous but anisotropic (Bianchi) universes. Here in this paper, we prove that arbitrarily inhomogeneous and anisotropic cosmologies with "flat'' (including toroidal) and "open'' (including compact hyperbolic) spatial topology that are initially expanding must continue to expand forever at least in some region at a rate bounded from below by a positive number, despite the presence of arbitrarily large density fluctuations and/or the formation of black holes. Because the set of 3-manifold topologies is countable, a single integer determines the ultimate fate of the universe, and, in a specific sense, most 3-manifolds are "flat" or "open". Our result has important implications for inflation: if there is a positive cosmological constant (or suitable inflationary potential) and initial conditions for the inflaton, cosmologies with "flat'' or "open" topology must expand forever in some region at least as fast as de Sitter space, and are therefore very likely to begin inflationary expansion eventually, regardless of the scale of the inflationary energy or the spectrum and amplitude of initial inhomogeneities and gravitational waves. Our result is also significant for numerical general relativity, which often makes use of periodic (toroidal) boundary conditions.},

doi = {10.1088/1475-7516/2016/10/022},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 10,

volume = 2016,

place = {United States},

year = {2016},

month = {10}

}

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