On the non-linear scale of cosmological perturbation theory

Expansion parameter∫ kσl 2 (k, z) ≡ 4π dq q 2 P lin (q, z)0Large kP 1−loop (k)P 2−loop (k)∼∼()1.14P lin (k, z) − 0.55k∂ k P lin (k, z) + 0.1[k∂ k ] 2 P lin (k, z) σl 2 (k, z)(2.14P lin (k, z) − 1.62k∂ k P lin (k, z) + 0.55[k∂ k ] 2 P lin (k, z))− 0.082[k∂ k ] 3 P lin (k, z) + 0.005[k∂ k ] 4 P lin (k, z) σl 4 (k, z)Small kP 1−loop (k) → − 61105 k 2 P lin (k, z) 4π 3∫ ∞P 2−loop (k) → − 44764143325 k 2 P lin (k, z) 4π 30dqP lin (q, z)∫ ∞where J(q) = 4π ∫ q0 dp p2 g(p/q)P lin (p, z) ∼ σ 2 l (q, z)Mathias Garny (DESY Hamburg / CERN)0dqP lin (q, z)J(q)On the non-linear scale of cosmological perturbation theory