Shape of the universe

The universe’s large-scale spatial geometry and topology, including its curvature, connectedness, and possible global form.

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Friedmann equations: Equations in relativistic cosmology that describe how the universe’s expansion changes over time. They connect cosmic expansion, energy content, and spatial curvature.
General relativity: Albert Einstein’s theory describing gravity as the curvature of spacetime caused by energy and matter. It supplies the gravitational framework for cosmological geometry.
Flat universe: A universe whose large-scale spatial curvature is zero. Measurements are consistent with near-zero curvature, but flatness does not fix topology.
Planck satellite: A European Space Agency observatory that mapped the cosmic microwave background from 2009 to 2013. Its measurements place strong constraints on curvature and primordial patterns.
Spatial curvature: A measure of how spatial geometry departs from Euclidean geometry. Positive, zero, or negative curvature distinguishes the main large-scale geometries.
Riemannian geometry: The mathematical study of spaces equipped with a smoothly varying notion of distance. It provides the language for describing curved spatial slices.
Closed universe: A spatially finite universe with positive curvature in the standard homogeneous models. It illustrates a finite geometry without an edge.
Cosmic variance: The irreducible uncertainty caused by observing only one realization of a cosmic process. It limits how decisively sky patterns can distinguish global models.
Critical density: The energy density that makes spatial curvature zero in standard cosmological models. Comparing cosmic density with this value constrains curvature.
Cosmological principle: The assumption that the universe is homogeneous and isotropic on sufficiently large scales. It reduces possible cosmic geometries to highly symmetric cases.