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
Perturbative solution for the
matter density, in Fourier space
δ k = δ (1)
k
+ δ (2)
k
+ ...
Linear solution
δ (2)
k
=
Initial conditions δ (1)
k1
δ (1)
k2
= δ D ( k 1 + k 2 )P 0 (k 1 )
B0 and T0 vanish for
Gaussian initial conditions!
• 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
d 3 qF 2 ( k − q, q) δ (1)
δ (1)
k−q q
Quadratic nonlinear correction
δ (1)
k1
δ (1)
k2
δ (1)
k3
= δ D ( k 1 + k 2 + k 3 ) B 0 (k 1 ,k 2 ,k 3 )
δ (1)
k1
δ (1)
k2
δ (1)
k3
δ (1)
k4
= δ D ( k 1 + ... + k 4 ) T 0 ( k 1 , k 2 , k 3 , k 4 )
Perturbative solution for the
matter 3-point function
δδδ = δ (1) δ (1) δ (1) + δ (1) δ (1) δ (2) + ...
loop corrections
= B0 = 0 for Gaussian
initial conditions
non-zero bispectrum
induced by gravity!