# Loop quantum cosmology and the k=-1 Robertson-Walker model

## Abstract

The loop quantization of the negatively curved k=-1 Robertson-Walker model poses several technical challenges. We show that the issues can be overcome and a successful quantization is possible that extends the results of the k=0, +1 models in a natural fashion. We discuss the resulting dynamics and show that for a universe consisting of a massless scalar field, a bounce is predicted in the backward evolution in accordance with the results of the k=0, +1 models. We also show that the model predicts a vacuum repulsion in the high curvature regime that would lead to a bounce even for matter with vanishing energy density. We finally comment on the inverse volume modifications of loop quantum cosmology and show that, as in the k=0 model, the modifications depend sensitively on the introduction of a length scale which a priori is independent of the curvature scale or a matter energy scale.

- Authors:

- Institute for Gravitational Physics and Geometry, Pennsylvania State University, University Park, Pennsylvania 16802 (United States)
- (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 20935219

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.75.023523; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COSMOLOGY; ENERGY DENSITY; GALACTIC EVOLUTION; MATTER; QUANTIZATION; QUANTUM GRAVITY; SCALAR FIELDS; UNIVERSE

### Citation Formats

```
Vandersloot, Kevin, and Institute for Cosmology and Gravitation, University of Portsmouth, Portsmouth, PO1 2EG.
```*Loop quantum cosmology and the k=-1 Robertson-Walker model*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.023523.

```
Vandersloot, Kevin, & Institute for Cosmology and Gravitation, University of Portsmouth, Portsmouth, PO1 2EG.
```*Loop quantum cosmology and the k=-1 Robertson-Walker model*. United States. doi:10.1103/PHYSREVD.75.023523.

```
Vandersloot, Kevin, and Institute for Cosmology and Gravitation, University of Portsmouth, Portsmouth, PO1 2EG. Mon .
"Loop quantum cosmology and the k=-1 Robertson-Walker model". United States.
doi:10.1103/PHYSREVD.75.023523.
```

```
@article{osti_20935219,
```

title = {Loop quantum cosmology and the k=-1 Robertson-Walker model},

author = {Vandersloot, Kevin and Institute for Cosmology and Gravitation, University of Portsmouth, Portsmouth, PO1 2EG},

abstractNote = {The loop quantization of the negatively curved k=-1 Robertson-Walker model poses several technical challenges. We show that the issues can be overcome and a successful quantization is possible that extends the results of the k=0, +1 models in a natural fashion. We discuss the resulting dynamics and show that for a universe consisting of a massless scalar field, a bounce is predicted in the backward evolution in accordance with the results of the k=0, +1 models. We also show that the model predicts a vacuum repulsion in the high curvature regime that would lead to a bounce even for matter with vanishing energy density. We finally comment on the inverse volume modifications of loop quantum cosmology and show that, as in the k=0 model, the modifications depend sensitively on the introduction of a length scale which a priori is independent of the curvature scale or a matter energy scale.},

doi = {10.1103/PHYSREVD.75.023523},

journal = {Physical Review. D, Particles Fields},

number = 2,

volume = 75,

place = {United States},

year = {Mon Jan 15 00:00:00 EST 2007},

month = {Mon Jan 15 00:00:00 EST 2007}

}