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Scalar mode −u ′′ +s(α) 2 ∆u+(˜z ′′ /˜z)u = 0 [with G Calcagni, S Tsujikawa 2011] 1 x 10−4 0.9 0.8 10 −8 < δ = α−1 < 10 −4 0.7 0.6 much closer than δ (k 0 ) 0.5 0.4 0.3 0.2 0.1 l P and l H 0 0 0.005 0.01 ε (k ) V 0 0.015 0.02 CCCC – p. 20
CCCC – p. 21 Holonomy corrections Hypersurface-deformation algebra with pointwise holonomy corrections: H −→ l −1 sin(lH) in perturbative cosmology. Incomplete: Corrections in series expansion cannot be separated from higher space and time derivatives. (R ∼ ∂Γ+Γ 2 ) with β = cos(2lH). [S(⃗w 1 ),S(⃗w 2 )] = −S(L ⃗w2 ⃗w 1 ) [T(N),S(⃗w)] = −T(⃗w · ⃗∇N) [T(N 1 ),T(N 2 )] = S(β(N 1 ⃗ ∇N2 −N 2 ⃗ ∇N1 )) −w ′′ +β∆w +(ã ′′ /ã)w = 0 β = −1 at maximal density (maximum of sin(lH), “bounce”). [J Reyes 2009; A Barrau, T Cailleteau, J Grain, J Mielczarek 2011]
Page 1 and 2: CCCC - p. 1 Covariant Canonical Cwa
Page 3 and 4: CCCC - p. 3 Loop quantum gravity
Page 5 and 6: CCCC - p. 5 Hypersurface-deformatio
Page 7 and 8: CCCC - p. 7 Energy conservation [wi
Page 9 and 10: CCCC - p. 9 Effective canonical dyn
Page 11 and 12: CCCC - p. 11 Low energy effective a
Page 13 and 14: CCCC - p. 13 Effective constraints
Page 15 and 16: CCCC - p. 15 Relevance of effective
Page 17 and 18: CCCC - p. 17 Deformed deformations
Page 19: CCCC - p. 19 Cosmological perturbat
Page 23 and 24: CCCC - p. 23 Ill-posed bounce Bounc
Page 25: CCCC - p. 25 Models of quantum spac

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