Adjust dark energy and matter densities to see how the universe expands—watch radiation, matter, and Λ dominate at different epochs
The ΛCDM (Lambda Cold Dark Matter) model is the standard model of cosmology. It describes a universe containing ordinary matter, dark matter, and dark energy (the cosmological constant Λ). The model explains the observed expansion history, from the radiation-dominated early universe through matter domination to the current dark-energy-dominated accelerating expansion.
The top panel shows the scale factor a(t) as a function of cosmic time. The scale factor measures how distances between galaxies grow: a=1 today, a=0 at the Big Bang, and a>1 in the future. The curve's shape reveals the expansion history: radiation domination (a∝t1/2), matter domination (a∝t2/3), and dark energy domination (exponential growth). A steepening curve means accelerating expansion; a flattening curve means deceleration.
The bottom panel shows how the energy budget changes with redshift. Matter density dilutes as ρ_m ∝ a-3 (volume expansion). Radiation dilutes faster as ρ_r ∝ a-4 (volume plus redshift). Dark energy (Λ) stays constant. Early on, radiation dominates; later matter takes over; eventually dark energy wins. The crossover epochs determine the universe's fate.
The sum Ωtotal = Ω_m + ΩΛ + Ω_r determines spatial curvature. Ω_total = 1 is flat (Euclidean geometry). Ω_total > 1 is closed (positive curvature, finite volume). Ω_total < 1 is open (negative curvature, infinite). Observations show our universe is remarkably flat: Ω_total ≈ 1.00. This is the "flatness problem" that motivates inflation.
The expansion is governed by the Friedmann equation: (ȧ/a)² = (8πG/3)ρ - k/a², where ȧ/a is the Hubble parameter H(t), ρ is the total energy density, and k is the spatial curvature. In terms of density parameters: H(z)² = H₀²[Ωm(1+z)³ + Ω_r(1+z)⁴ + ΩΛ + Ω_k(1+z)²]. This single equation encodes the universe's entire expansion history from the Big Bang to the far future.
Current Universe: Set Ωm = 0.30, ΩΛ = 0.70. This is the measured composition today. Notice the expansion accelerates in the late universe (curve steepens) due to dark energy dominance. The age is about 13.8 Gyr. Without dark energy, the universe would be younger.
Matter-Only Universe: Set Ωm = 1.0, ΩΛ = 0. The expansion decelerates forever (a∝t2/3). No acceleration, no future exponential growth. This was the favored model before 1998 when dark energy was discovered via Type Ia supernovae.
Pure Dark Energy: Set Ωm = 0, ΩΛ = 1.0. The scale factor grows exponentially: a(t) ∝ exp(H₀t). This is de Sitter space—empty except for vacuum energy. Our universe's far future resembles this: all matter becomes negligibly dilute, and only dark energy remains.
Open Universe: Set Ωm = 0.3, ΩΛ = 0.5 (total < 1). The universe has negative spatial curvature—saddle-shaped geometry. Parallel lines diverge. Triangles have angle sums less than 180°. The universe expands forever and eventually approaches linear expansion a∝t.
Closed Universe: Set Ωm = 0.7, ΩΛ = 0.5 (total > 1). Positive curvature—spherical geometry. Parallel lines converge. Depending on the balance, it might recollapse (Big Crunch), but with enough Λ it can still expand forever despite being closed.
Radiation Era: Set Ωr = 0.05, Ω_m = 0.3, ΩΛ = 0.65. Watch the composition plot: at very high redshift (z>3000, recombination epoch), radiation briefly dominates. In the first ~50,000 years, the universe was radiation-dominated with a∝t1/2. This era shaped the CMB and nucleosynthesis.
The ΛCDM model is our best description of cosmic history. It explains:
Yet ΛCDM has mysteries. We don't know what dark matter is (CDM = Cold Dark Matter, non-baryonic particles). We don't know why dark energy has the value it does (the "cosmological constant problem"—theory predicts 10120 times too large!). And we don't know if Λ is truly constant or slowly evolving. Despite these puzzles, ΛCDM fits all observations with just six parameters. It is a triumph of theoretical cosmology and observational astronomy.