On the non-linear scale of cosmological perturbation theory

Standard Perturbation TheoryPoisson/Euler/Continuity eq. for density contrast δ = ρ/¯ρ − 1 and pec.velocity (neglect vorticity/viscosity → talks by Mercolli, Zaldarriaga)Expand solution in δ 0(k) = δ(k, z 0 ∼ 10 3 ), for EdS / growing modeδ(k, z) =∞∑(D +(z))∫q n δ (3) (k − ∑ q i )F n(q 1, . . . , q n)δ 0(q 1) · · · δ 0(q n)in=1= D +(z)δ 0(k) + . . .( )e.g. F2 s (q 1, q 2) = 5 + 1 q 1·q 2 q17 2 q 1 q 2 q 2+ q 2q 1+ 2 (q 1·q 2 ) 27 q1 2q2 2Power spectrum 〈δ(k, z)δ(k ′ , z)〉 = δ (3) (k + k ′ )P(k, z) is obtained usingWick theorem in terms of P 0(q) = P(q, z 0) for Gaussian ICP(k, z) =P 1−loopP lin{ }} { { }} {D +(z) 2 P 0(k) + D +(z) 4 (2P 13 + P 22)+ D +(z) 6 (2P 15 + 2P 24 + P 33) + . . .e.g. P 22(k) = 2 ∫ d 3 q F s 2 (q, k − q) 2 P 0(q)P 0(|k − q|)Mathias Garny (DESY Hamburg / CERN)On the non-linear scale of cosmological perturbation theory