Slides from the talk - CP3-Origins

Non-Gaussianity from Gravitational Instability
At large scales fluctuations are small, σδ≪1, even at low redshift
we can study their evolution in terms of Perturbation Theory
Equations of motion for
matter density and velocity:
δ, v
• Continuity eq.
• Euler eq.
• Poisson eq.
∂δ
+ ∇ · [(1 + δ)v] =0
∂τ
∂v
∂τ + Hv +(v · ∇)v = −∇φ
∇ 2 φ = 3 2 H2 Ω m δ
Perturbative solution for the
matter density, in Fourier space
δ k = δ (1)
k
+ δ (2)
k
+ ...
Linear solution
δ (2)
k
=
d 3 qF 2 ( k − q, q) δ (1)
δ (1)
k−q q
Quadratic nonlinear correction