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CCCC – p. 18 Space-time? Deformed gauge algebra implies that <strong>the</strong>ory is no longer invariant under space-time diffeomorphisms. Same number of gauge generators: <strong>the</strong>ory remains consistent. Can be evaluated with canonical methods (Hamiltonian equations of motion, gauge transformations, observables, . . . ). But no analog of space-time metric or line element: ds 2 = g ab dx a dx b not invariant since transformations of g ab and dx a no longer match. (Warning for homogeneous models or perturbations: Often, “effective” FLRW metric −dt 2 +a(t) 2 (dx 2 +dy 2 +dz 2 ) assumed with a(t) subject to modified Friedmann equation.)
CCCC – p. 19 Cosmological perturbation equations [with G Calcagni: arXiv:1011.2779] Dynamics of density perturbations u, gravitational waves w: −u ′′ +s(α) 2 ∆u+(˜z ′′ /˜z)u = 0 −w ′′ +α 2 ∆w +(ã ′′ /ã)w = 0 Wave equations. Corrections to tensor-to-scalar ratio. 2.5 2 Do not need high density. Crucial for falsifiability: α−1 large for small lattice spacing. Two-sided bounds on discreteness scale. α (r) 1.5 1 0.5 0 0 0.5 1 1.5 2 µ r=1/2 r=3/4 r=1 r=3/2 r=2
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: CCCC - p. 17 Deformed deformations
Page 21 and 22: CCCC - p. 21 Holonomy corrections H
Page 23 and 24: CCCC - p. 23 Ill-posed bounce Bounc
Page 25: CCCC - p. 25 Models of quantum spac

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