Cosmology

The shape and fate of the entire universe

The Universe Itself

General relativity doesn't just describe black holes and orbits — it governs the evolution of the entire universe. The Friedmann equations, derived directly from Einstein's field equations, predict an expanding (or contracting) universe. The discovery that our universe is not only expanding but accelerating is one of the great mysteries of modern physics.

Friedmann Equation Explorer

The scale factor a(t) describes how the universe expands over time. Its behavior depends on the universe's composition: matter, radiation, dark energy, and spatial curvature. Adjust the density parameters to see expanding, decelerating, accelerating, and even collapsing universes.

Click presets to overlay cosmological models. The amber dot marks the present epoch (a=1, t=0).

Try it: Our universe has Ω_m ≈ 0.3, Ω_Λ ≈ 0.7. Set these values to see the expansion history. Then try Ω_m = 1 (Einstein-de Sitter) or Ω_m > 1 (Big Crunch) to see the dramatic alternatives.

Cosmic Redshift

As the universe expands, the wavelength of light stretches with it. A photon emitted by a distant galaxy arrives at Earth with a longer wavelength — shifted toward the red end of the spectrum. The redshift z tells us how much the universe has expanded since the light was emitted: 1 + z = a(now)/a(then).

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As space expands, photon wavelengths stretch (redshift). Higher z means more expansion since emission.

The Shape of Space

General relativity allows three possible spatial geometries for the universe: flat (k = 0, parallel lines stay parallel), spherical (k = +1, parallel lines converge), and hyperbolic (k = -1, parallel lines diverge). Observations indicate our universe is very nearly flat.

Parallel lines stay parallel forever. Euclidean geometry.

Observable Universe & Horizons

The observable universe has a finite size — about 46 billion light-years in radius — even though the universe may be infinite. The particle horizon is the farthest distance from which light has had time to reach us. The event horizon is the distance beyond which light emitted now will never reach us.

Particle horizonEvent horizonCMB

Conformal spacetime diagram. The particle horizon bounds what we can see; the event horizon bounds what we can ever reach.

Key Takeaways

  • Friedmann equations — Govern the expansion of the universe; derived from Einstein's field equations
  • Cosmic redshift — Light stretches as the universe expands; z encodes expansion history
  • Spatial geometry — The universe can be flat, spherical, or hyperbolic; observations favor flat
  • Horizons — The observable universe is finite even if the universe itself is infinite