Gravity vs. cosmic expansion

The growth of large-scale structure as a tug of war: gravity amplifies primordial wrinkles into the cosmic web while the expansion drags against it. Same initial conditions, three referees — scrub cosmic time, or press play.

ln a

a = 1.00 · z = 0.00 · D = 0.78 · Ωm(a) = 0.30

Growth rate f = dlnD/dlna 0.51

Gravity source · (3/2) Ωm(a)0.45

Hubble drag · (2 + dlnH/dlna) f0.80

Model: linear growth ODE D″ + (2 + dlnH/dlna) D′ = (3/2) Ωm(a) D, RK4-integrated in N = ln a from z = 49 to z = −0.75 for flat matter+Λ backgrounds (radiation neglected; <1% in H at the start). Normalization: growing-mode initial conditions with D → a in matter domination, so all three models share primordial amplitudes and EdS is exactly D = a. Particles: 2D Zel’dovich displacements x = q + D(a) ψ(q); shell crossing is regularized adhesion-style, D_eff = min(D, −1/λ₁), and brightness scales with the log of 1/[(1+D_eff λ₁)(1+D_eff λ₂)]. Keyboard: space plays/pauses, arrow keys scrub. Single file, no dependencies.