# Inflationary quantum cosmology: General framework and exact Bianchi type I solution

## Abstract

Using the methods of loop quantum gravity, we derive a framework for describing an inflationary, homogeneous universe in a purely quantum theory. The classical model is formulated in terms of the Ashtekar-Sen connection variables for a general subclass of Bianchi class A spacetimes. This formulation then provides a means to develop a corresponding quantum theory. An exact solution is derived for the classical Bianchi type I model and the corresponding semiclassical quantum state is found to also be an exact solution to the quantum theory. The development of a normalizable quantum state from this exact solution is presented and the implications for the normalizability of the Kodama state discussed. We briefly consider some consequences of such a quantum cosmological framework and show that the quantum scale factor of the universe has a continuous spectrum in this model. This result may suggest further modifications that are required to build a more accurate theory. We close this study by suggesting a variety of directions in which to take the results presented.

- Authors:

- Perimeter Institute for Theoretical Physics, Waterloo (Canada)

- Publication Date:

- OSTI Identifier:
- 20705510

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. D, Particles Fields

- Additional Journal Information:
- Journal Volume: 70; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.70.084040; (c) 2004 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COSMOLOGY; EXACT SOLUTIONS; QUANTUM GRAVITY; SEMICLASSICAL APPROXIMATION; SPACE-TIME; UNIVERSE

### Citation Formats

```
Malecki, Justin.
```*Inflationary quantum cosmology: General framework and exact Bianchi type I solution*. United States: N. p., 2004.
Web. doi:10.1103/PhysRevD.70.084040.

```
Malecki, Justin.
```*Inflationary quantum cosmology: General framework and exact Bianchi type I solution*. United States. doi:10.1103/PhysRevD.70.084040.

```
Malecki, Justin. Fri .
"Inflationary quantum cosmology: General framework and exact Bianchi type I solution". United States. doi:10.1103/PhysRevD.70.084040.
```

```
@article{osti_20705510,
```

title = {Inflationary quantum cosmology: General framework and exact Bianchi type I solution},

author = {Malecki, Justin},

abstractNote = {Using the methods of loop quantum gravity, we derive a framework for describing an inflationary, homogeneous universe in a purely quantum theory. The classical model is formulated in terms of the Ashtekar-Sen connection variables for a general subclass of Bianchi class A spacetimes. This formulation then provides a means to develop a corresponding quantum theory. An exact solution is derived for the classical Bianchi type I model and the corresponding semiclassical quantum state is found to also be an exact solution to the quantum theory. The development of a normalizable quantum state from this exact solution is presented and the implications for the normalizability of the Kodama state discussed. We briefly consider some consequences of such a quantum cosmological framework and show that the quantum scale factor of the universe has a continuous spectrum in this model. This result may suggest further modifications that are required to build a more accurate theory. We close this study by suggesting a variety of directions in which to take the results presented.},

doi = {10.1103/PhysRevD.70.084040},

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

issn = {0556-2821},

number = 8,

volume = 70,

place = {United States},

year = {2004},

month = {10}

}