What is the density parameter $\Omega$ for a geometrically flat universe?

$\Omega = 1$

The geometry of the universe is fundamentally classified by its curvature, which is mathematically linked to the density parameter, $\Omega$, representing the total mass and energy content. A flat universe corresponds precisely to the condition where the actual density equals the critical density, meaning $\Omega$ must be exactly 1. When $\Omega$ equals 1, the geometry adheres to Euclidean principles. This means that familiar geometric rules apply perfectly across vast scales; for example, parallel lines established in this space will never converge or meet, and the interior angles of any sufficiently large triangle drawn through spacetime will sum up to exactly 180 degrees. This specific value of $\Omega=1$ is the critical threshold separating open and closed geometries.