On the non-linear scale of cosmological perturbation theory

Basic formalism for large scale structureDensity contrast ρ(x, τ) = ¯ρ(τ)(1 + δ(x, τ)), pec. velocity u(x, τ)1st and 2nd moment of Vlasov eq. for f (x, p, τ), neglect multi-streaming(pressure, stress/viscosity → talks by Mercolli, Zaldarriaga)∂δ(x, τ)∂τ+ ∇ · {(1 + δ(x, τ)u(x, τ)} = 0 (continuity)∂u(x, τ)∂τ+ Hu + u · ∇u = −∇Φ (Euler)∇ 2 Φ(x, τ) = 3 2 ΩmH2 δ(x, τ) (Poisson)neglect vorticity ∇ × u ≈ 0 ⇒ sufficient to use θ = ∇ · usolution of linearized eqs (D + ∼ a, D − ∼ a −3/2 in EdS)Power spectrum in Fourier spaceδ lin (x, τ) = D +(τ)δ 0(x) + O(D −)〈δ(k, τ)δ(k ′ , τ)〉 = δ (3) (k + k ′ )P(k, τ)assume Gaussian IC described by P 0(k) = P(k, τ 0)Mathias Garny (DESY Hamburg / CERN)On the non-linear scale of cosmological perturbation theory