Every glowing point is a galaxy sitting at a fixed comoving position; what moves it apart from its neighbours is the scale factor a(t) stretching the space between them — the galaxies themselves aren't flying outward, the metric is expanding. a(t) is evolved by integrating the flat Friedmann equation forward from a hot, dense a≈0 state:
(ȧ/a)² = H(a)² = H₀² [ Ω_m·a⁻³ + Ω_Λ·a⁻³⁽¹⁺w⁾ ]
ä/a = −(H₀²/2) [ Ω_m·a⁻³ + (1+3w)·Ω_Λ·a⁻³⁽¹⁺w⁾ ]
The second line is what actually decides whether expansion speeds up or slows down: matter (w=0) always pulls the universe back together via gravity, while dark energy with w < −1/3 contributes a repulsive term that can overwhelm it once the universe is dilute enough — that's the accelerated expansion discovered from 1998 Type Ia supernovae. A cosmological constant is the special case w = −1, ΩΛ constant in density as the universe grows; "quintessence" is −1<w<−1/3; "phantom" dark energy is w<−1, which grows ever more dominant and can eventually tear even bound structures apart.
- Ω_m — matter's share of the critical density today; higher Ω_m means more gravitational pull working against expansion.
- Ω_Λ — dark energy's share of the critical density; set it to 0 for a matter-only universe (no acceleration, ever).
- w — dark energy's equation of state (pressure/density); −1 is a true cosmological constant, more negative ("phantom") accelerates harder.
- Time speed — how fast cosmic time advances in the animation; the physics itself doesn't change.
The inset graph tracks a(t) for your current settings (violet) against a pure matter universe with the same starting point (grey, Ω_m=1, Ω_Λ=0) — the real universe's curve visibly bends upward as dark energy takes over, while the matter-only curve keeps decelerating forever.