### Abstract

A gauge-invariant quantum theory of the Friedmann-Robertson-Walker (FRW) universe with dust is studied in terms of the Ashtekar variables. We use the reduced phase space quantization which has following advantages: (i) fundamental variables are all gauge invariant, (ii) there exists a physical time evolution of gauge-invariant quantities, so that the problem of time is absent, and (iii) the reduced phase space can be quantized in the same manner as in ordinary quantum mechanics. In the FRW model, the dynamical components of the Ashtekar variables are given by a single quantity p and its conjugate momentum, where p is related to the scale factor a as a?√|p| and its sign gives the orientation of triads. We solve a scattering problem in terms of ingoing and outgoing energy eigenstates. We show that the incident wave is reflected in rate 1/4 and transmitted in rate 3/4 at the classical singularity p=0. Analyzing the dynamics of a wave packet, we show that the classical initial singularity is replaced by a big bounce in quantum theory. A possible interpretation of the result is that the wave function of the universe has been in a superposition of states representing right-handed and left-handed systems before the big bounce.

Original language | English |
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Article number | 104007 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 82 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2010 Nov 3 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**Big bounce as the scattering of the wave function at the big crunch.** / Amemiya, Fumitoshi; Koike, Tatsuhiko.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 82, no. 10, 104007. https://doi.org/10.1103/PhysRevD.82.104007

}

TY - JOUR

T1 - Big bounce as the scattering of the wave function at the big crunch

AU - Amemiya, Fumitoshi

AU - Koike, Tatsuhiko

PY - 2010/11/3

Y1 - 2010/11/3

N2 - A gauge-invariant quantum theory of the Friedmann-Robertson-Walker (FRW) universe with dust is studied in terms of the Ashtekar variables. We use the reduced phase space quantization which has following advantages: (i) fundamental variables are all gauge invariant, (ii) there exists a physical time evolution of gauge-invariant quantities, so that the problem of time is absent, and (iii) the reduced phase space can be quantized in the same manner as in ordinary quantum mechanics. In the FRW model, the dynamical components of the Ashtekar variables are given by a single quantity p and its conjugate momentum, where p is related to the scale factor a as a?√|p| and its sign gives the orientation of triads. We solve a scattering problem in terms of ingoing and outgoing energy eigenstates. We show that the incident wave is reflected in rate 1/4 and transmitted in rate 3/4 at the classical singularity p=0. Analyzing the dynamics of a wave packet, we show that the classical initial singularity is replaced by a big bounce in quantum theory. A possible interpretation of the result is that the wave function of the universe has been in a superposition of states representing right-handed and left-handed systems before the big bounce.

AB - A gauge-invariant quantum theory of the Friedmann-Robertson-Walker (FRW) universe with dust is studied in terms of the Ashtekar variables. We use the reduced phase space quantization which has following advantages: (i) fundamental variables are all gauge invariant, (ii) there exists a physical time evolution of gauge-invariant quantities, so that the problem of time is absent, and (iii) the reduced phase space can be quantized in the same manner as in ordinary quantum mechanics. In the FRW model, the dynamical components of the Ashtekar variables are given by a single quantity p and its conjugate momentum, where p is related to the scale factor a as a?√|p| and its sign gives the orientation of triads. We solve a scattering problem in terms of ingoing and outgoing energy eigenstates. We show that the incident wave is reflected in rate 1/4 and transmitted in rate 3/4 at the classical singularity p=0. Analyzing the dynamics of a wave packet, we show that the classical initial singularity is replaced by a big bounce in quantum theory. A possible interpretation of the result is that the wave function of the universe has been in a superposition of states representing right-handed and left-handed systems before the big bounce.

UR - http://www.scopus.com/inward/record.url?scp=78651265506&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78651265506&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.82.104007

DO - 10.1103/PhysRevD.82.104007

M3 - Article

AN - SCOPUS:78651265506

VL - 82

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 10

M1 - 104007

ER -