The Geometry of the Universe – Flat, Open, or Closed?

Cosmologists measure the shape of the universe using curvature: flat (Euclidean, zero curvature), spherical (positive curvature, closed, finite), or hyperbolic (negative curvature, open, infinite). The Planck satellite measured the cosmic microwave background and found the universe is flat to within 0.4%. But flatness is unstable – why so flat? Inflation theory explains it. The geometry is encoded in the Friedmann equations (general relativity). The total density parameter Ω₀ ≈ 1.00 exactly. Our observable universe is a tiny patch of a possibly infinite, flat expanse.