### Abstract

The Wheeler-DeWitt equation is developed from the Einstein-Hilbert action where the gravity is coupled to the mass-energy and scalar field. The wave function of the universe in Wheeler-DeWitt equation is written in polar form. Subsequently, we obtain the modified Friedmann equation. We then proceed to present the derivation of a more simplified version of modified Friedmann equations where the gravitational part of Einstein-Hilbert action is coupled only to mass-energy. These simplified version of modified first and second Friedmann equations have additional terms which contain the quantum potential energy. We then take an ansatz for the form of amplitude function and find that if the inflationary expansion really happens in the early universe, our universe (for simplicity, spatial curvature k=0) might start to evolve from a non-singularity. Keywords: Canonical quantum cosmology, de Broglie-Bohm interpretation, Modified Friedmann equations, Wheeler-DeWitt equation.

Original language | English |
---|---|

Pages (from-to) | 121-138 |

Number of pages | 18 |

Journal | Advanced Studies in Theoretical Physics |

Volume | 9 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2015 |

### Fingerprint

### Keywords

- Canonical quantum cosmology
- De Broglie-bohm interpretation
- Modified Friedmann equations
- Wheeler-DeWitt equation

### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

*Advanced Studies in Theoretical Physics*,

*9*(3), 121-138. https://doi.org/10.12988/astp.2015.412158

**The modified Friedmann equations.** / Siong, Ch’Ng Han; Radiman, Shahidan.

Research output: Contribution to journal › Article

*Advanced Studies in Theoretical Physics*, vol. 9, no. 3, pp. 121-138. https://doi.org/10.12988/astp.2015.412158

}

TY - JOUR

T1 - The modified Friedmann equations

AU - Siong, Ch’Ng Han

AU - Radiman, Shahidan

PY - 2015

Y1 - 2015

N2 - The Wheeler-DeWitt equation is developed from the Einstein-Hilbert action where the gravity is coupled to the mass-energy and scalar field. The wave function of the universe in Wheeler-DeWitt equation is written in polar form. Subsequently, we obtain the modified Friedmann equation. We then proceed to present the derivation of a more simplified version of modified Friedmann equations where the gravitational part of Einstein-Hilbert action is coupled only to mass-energy. These simplified version of modified first and second Friedmann equations have additional terms which contain the quantum potential energy. We then take an ansatz for the form of amplitude function and find that if the inflationary expansion really happens in the early universe, our universe (for simplicity, spatial curvature k=0) might start to evolve from a non-singularity. Keywords: Canonical quantum cosmology, de Broglie-Bohm interpretation, Modified Friedmann equations, Wheeler-DeWitt equation.

AB - The Wheeler-DeWitt equation is developed from the Einstein-Hilbert action where the gravity is coupled to the mass-energy and scalar field. The wave function of the universe in Wheeler-DeWitt equation is written in polar form. Subsequently, we obtain the modified Friedmann equation. We then proceed to present the derivation of a more simplified version of modified Friedmann equations where the gravitational part of Einstein-Hilbert action is coupled only to mass-energy. These simplified version of modified first and second Friedmann equations have additional terms which contain the quantum potential energy. We then take an ansatz for the form of amplitude function and find that if the inflationary expansion really happens in the early universe, our universe (for simplicity, spatial curvature k=0) might start to evolve from a non-singularity. Keywords: Canonical quantum cosmology, de Broglie-Bohm interpretation, Modified Friedmann equations, Wheeler-DeWitt equation.

KW - Canonical quantum cosmology

KW - De Broglie-bohm interpretation

KW - Modified Friedmann equations

KW - Wheeler-DeWitt equation

UR - http://www.scopus.com/inward/record.url?scp=84929165056&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84929165056&partnerID=8YFLogxK

U2 - 10.12988/astp.2015.412158

DO - 10.12988/astp.2015.412158

M3 - Article

AN - SCOPUS:84929165056

VL - 9

SP - 121

EP - 138

JO - Advanced Studies in Theoretical Physics

JF - Advanced Studies in Theoretical Physics

SN - 1313-1311

IS - 3

ER -