What the Universe Is Made Of

Part 4: What Shape Is Space?

The curvature term decides the geometry. Add up all the densities: if the total equals the critical density, $\Omega_\text{total} = 1$, the curvature term vanishes and space is flat — ordinary Euclidean geometry, where parallel lines stay parallel and triangles’ angles sum to $180°$. If $\Omega_\text{total} > 1$ the universe is closed (positively curved, like a sphere’s surface generalized to three dimensions); if $\Omega_\text{total} \lt 1$ it is open (negatively curved, saddle-like).

The geometry is not a matter of taste — the CMB measures it. The characteristic size of the temperature ripples is a known physical scale; how large it appears on the sky depends on whether the intervening space is flat, closed, or open. The answer is decisive: $\Omega_\text{total} = 1.00$ to within a percent. Space is flat, which is why the budget closes at exactly $1$.