Cosmic Expansion

What to watch for

The Cosmic fate selector snaps the densities to the four textbook universes, and the $a(\tau)$ curve below the field tells you which future you have chosen:

• An open universe ($\Omega_M < 1$, no $\Lambda$) has positive curvature energy to spare. Gravity slows it but never wins: $a$ rises forever, ever more slowly.
• The flat Einstein–de Sitter case ($\Omega_M = 1$) sits exactly on the knife-edge: it expands without limit, but the rate $\dot a$ creeps towards zero.
• A closed universe ($\Omega_M > 1$) has enough matter to halt the expansion. Watch $a$ rise, stall at a maximum, then reverse: gravity drags everything back to a Big Crunch, and the simulation rebounds to do it again.
• Switch on a cosmological constant ($\Lambda$ accelerating, $\Omega_M + \Omega_\Lambda \approx 1$) and the curve turns upward: once the thinning matter can no longer hold dark energy back, the expansion accelerates. This is our universe: flat, matter-light, and running away.

Notice that with $\Lambda$ on, redshifts climb without bound as the runaway expansion stretches light from ever-receding galaxies. In the recollapsing closed model the redshift first grows, then would turn to a blueshift on the way down as the gaps shrink again.

Knobs

• Cosmic fate: picks one of the four canonical universes (open, flat, closed, or $\Lambda$-accelerating) and loads its density mix. Dragging either density slider away from a preset relabels the fate to match what you have dialled.
• Ω_M (matter): the present-day matter density relative to the critical density. More matter means stronger gravity: it slows the expansion and, if large enough, forces a recollapse.
• Ω_Λ (dark energy) — the cosmological-constant density. Even a modest amount eventually dominates the diluting matter and tips the universe into accelerating expansion.
• H₀ (expansion rate) — the Hubble constant, here a dimensionless playback rate. It sets how fast cosmic time runs in the animation without changing which fate you are heading towards.