# Absence of a Singularity in Loop Quantum Cosmology

## Abstract

It is shown that the cosmological singularity in isotropic minisuperspaces is naturally removed by quantum geometry. Already at the kinematical level, this is indicated by the fact that the inverse scale factor is represented by a bounded operator even though the classical quantity diverges at the initial singularity. The full demonstration comes from an analysis of quantum dynamics. Because of quantum geometry, the quantum evolution occurs in discrete time steps and does not break down when the volume becomes zero. Instead, space-time can be extended to a branch preceding the classical singularity independently of the matter coupled to the model. For large volume the correct semiclassical behavior is obtained.

- Authors:

- Publication Date:

- Sponsoring Org.:
- (US)

- OSTI Identifier:
- 40203645

- Alternate Identifier(s):
- OSTI ID: 40203645

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review Letters

- Additional Journal Information:
- Journal Volume: 86; Journal Issue: 23; Other Information: DOI: 10.1103/PhysRevLett.86.5227; Othernumber: PRLTAO000086000023005227000001; 012124PRL; PBD: 4 Jun 2001; Journal ID: ISSN 0031-9007

- Publisher:
- The American Physical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COSMOLOGY; GEOMETRY; SINGULARITY; SPACE-TIME

### Citation Formats

```
Bojowald, Martin.
```*Absence of a Singularity in Loop Quantum Cosmology*. United States: N. p., 2001.
Web. doi:10.1103/PhysRevLett.86.5227.

```
Bojowald, Martin.
```*Absence of a Singularity in Loop Quantum Cosmology*. United States. doi:10.1103/PhysRevLett.86.5227.

```
Bojowald, Martin. Mon .
"Absence of a Singularity in Loop Quantum Cosmology". United States. doi:10.1103/PhysRevLett.86.5227.
```

```
@article{osti_40203645,
```

title = {Absence of a Singularity in Loop Quantum Cosmology},

author = {Bojowald, Martin},

abstractNote = {It is shown that the cosmological singularity in isotropic minisuperspaces is naturally removed by quantum geometry. Already at the kinematical level, this is indicated by the fact that the inverse scale factor is represented by a bounded operator even though the classical quantity diverges at the initial singularity. The full demonstration comes from an analysis of quantum dynamics. Because of quantum geometry, the quantum evolution occurs in discrete time steps and does not break down when the volume becomes zero. Instead, space-time can be extended to a branch preceding the classical singularity independently of the matter coupled to the model. For large volume the correct semiclassical behavior is obtained.},

doi = {10.1103/PhysRevLett.86.5227},

journal = {Physical Review Letters},

issn = {0031-9007},

number = 23,

volume = 86,

place = {United States},

year = {2001},

month = {6}

}

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