Contrasting LQC and WDW Theory Using an Exactly Solvable Model

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Volume observable in S<strong>LQC</strong> (χ, ˆ V |φ χ)phy = 8γℓ2 P λ2 √ 12πG ∞ + ∞ dx− −∞ dx+ dχ− dx− −∞ = I+ e −√ √ 12πGφ 12πGφ + I− e 2 dχ+ 2 dx+ cosh( √ 12πG(x+ − φ)) cosh( √ 12πG(−x− + φ)) There exists a minimum value of 〈V | (φ=φB)〉 which occurs at φB = (2 √ 12πG) −1 ln(I+/I−) 〈V |φ〉 is symmetric across the bounce point. IGC Inaugural Conference – p.7
Fluctuations 〈V 2 |φ〉 = J0 + J+e −2√ 12πGφ + J−e 2√ 12πGφ is symmetric across Relative dispersion: φ ′ B = (4 √ 12πG) −1 ln(J+/J−) (∆V/〈 ˆ V 〉) 2 φ→∞ = J− I 2 − (∆V/〈 ˆ V 〉) 2 φ→−∞ = J+ I 2 + − 1 − 1 For φB = φ ′ B , D := (∆V/〈ˆ V 〉) 2 φ→−∞ − (∆V/〈ˆ V 〉) 2 φ→∞ = 0 Relative dispersion bounded in time evolution. A single condition on the infinite dimensional space of initial data implies symmetric fluctuations across bounce point. IGC Inaugural Conference – p.8
Page 1 and 2: New Insights in Loop Quantum Cosmol
Page 3 and 4: Motivation Extensive analytical and
Page 11 and 12: Hilbert space can be constructed fo
Page 13: Volume observable in WDW (χ, ˆ V
Page 17 and 18: How much does the Cosmos recall? Fo
Page 19 and 20: How much does the Cosmos recall? Co
Page 21 and 22: How much does the Cosmos recall? Co
Page 23 and 24: WDW & SLQC and the lack of continuu
Page 25 and 26: WDW & SLQC and the lack of continuu
Page 27 and 28: Summary Bounce not restricted to st
Page 29 and 30: Fundamental discreteness of SLQC St
Page 31 and 32: Fundamental discreteness of SLQC St

Contrasting LQC and WDW Theory Using an Exactly Solvable Model

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