Monday, 07/24: Writing a pm-code - AIP

Model equations 17
It is also convenient to choose the expansion factor as time variable (using
expressions for the Hubble constant: ȧ = aH(a)). For this choice of variables,
the Poisson equation and equations of motion can be re-written as
∇ 2 φ = 4πGΩ m,0 ρ crit,0 a −1 δ,
δ = ρ − ¯ρ
¯ρ ,
dp
da = −∇φ ȧ ,
dx
da =
p
ȧa 2.
where δ is the overdensity in comoving coordinates and ȧ is
ȧ = H 0 a −1/2 √Ω m,0 + Ω k,0 a + Ω Λ,0 a 3 ; Ω m,0 + Ω Λ,0 + Ω k,0 = 1