Dark Energy & Cosmic Expansion

Friedmann Equation — Scale Factor Evolution a(t)

The Friedmann equation (ȧ/a)² = H² = (8πG/3)(ρ_m + ρ_r + ρ_Λ) − kc²/a² governs the expansion of the universe. Dark energy (Λ) with equation of state w=−1 causes accelerating expansion. The scale factor a(t) ∝ t^2/3 (matter), ∝ t^1/2 (radiation), ∝ e^Ht (Λ-dominated). Current: Ω_Λ≈0.69, Ω_m≈0.31.

Ω_Λ (dark energy)

Ω_Λ = 0.69

Ω_m (matter)

Ω_m = 0.31

Ω_r (radiation)

Ω_r = 0.0001

w (dark energy eq. of state)

w = -1.00

Ω_total:—

Curvature k:—

Age (H₀t₀):—

Decel. param. q₀:—

Accel. today:—

Concordance ΛCDM

Matter dominated

Radiation dominated

Dark energy only

Today (a=1)