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Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高高高 / 高高高高高 Institute of Physics, Chiao Tung University

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Page 1: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University

Friedmann equation and quantum cosmology/ CMB for undergraduate

W.F. Kao, 高文芳 /交大物理所Institute of Physics,

Chiao Tung University

Page 2: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University

Outline

• Friedmann-Robertson-Walker metric/CMB

• Bianchi Identity and Redundancy

• Accetta, Zoller and Turner, PRD31, 3046 (1985)

• Randjbar-Daemi, A. Salam, Stradthdee, Phys. Lett. 135B, 388 (1984)

Page 3: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University

Referecence:

• Kao and Pen, PRD44, 3974 (1991)

• Dobado and Maroto, PRD52, 1895 (1995)

• Kao, Pen and Zhang, gr-qc/9911116

• Kao, PRD61, 047501 (2000)

• A. Vilenkin, PRD57, R7069 (2000)

Page 4: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University

Robert Wilson/Arno Penzias

Page 5: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University
Page 6: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University
Page 7: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University
Page 8: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University
Page 9: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University
Page 10: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University
Page 11: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University
Page 12: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University
Page 13: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University
Page 14: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University

Array for Microwave Background Anisotropy (AMIBA)

Page 15: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University

Friedmann-Robertson-Walker metric/CMB

factor scale

1

1[)(

(CMB) background microwave

cosmic shomogeneou and Isotropic

222

22

2

drdrkr

tadtds

function lapse

)( 2

tb

ed)(Generaliz

Page 16: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University

0

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Page 17: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University

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Page 18: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University
Page 19: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University

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Page 20: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University
Page 21: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University

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Page 22: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University

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Page 23: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University

vilenkin98.pdf

Page 24: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University

Hamiltonian Lagrangian

),,(),,(ˆ

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dt

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Page 25: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University

0 ˆ H

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densityenergy total

0

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Wheeler-DeWitt Equation

Universe as a quantum particle?Q.G. on FRW space/Mini-super-space

Page 26: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University

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momentum conjugate

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Page 27: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University

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Page 28: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University

aa 0

Page 29: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University

) exp(-3/8 exp

ion approximat under WKB ,0for

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Page 30: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University

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Page 31: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University

Gauge/Scale symmetry

Page 32: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University

thatdemands equations system the

thatprove alsocan one

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Page 33: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University
Page 34: Friedmann equation and quantum cosmology/ CMB for undergraduate W.F. Kao, 高文芳 / 交大物理所 Institute of Physics, Chiao Tung University

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