Age of the Universe from Hubble Constant
Estimate the age of the universe from the Hubble constant.
Calculate Hubble time and ΛCDM-corrected age.
Compare to the accepted value of 13.8 billion years.
Hubble time is the simplest estimate for the age of the universe:
t_H = 1 / H₀
This assumes the universe has been expanding at a constant rate — which it hasn’t.
Converting H₀ to SI units:
H₀ (1/s) = H₀ (km/s/Mpc) × 1000 / (3.0857 × 10²²)
1 Megaparsec = 3.0857 × 10²² meters.
ΛCDM correction: In the standard ΛCDM cosmological model (with dark matter and dark energy), the universe’s expansion was decelerating early on (matter-dominated) and is now accelerating (dark energy dominated). Accounting for this, the actual age is:
t₀ ≈ 0.964 / H₀
This gives ~13.8 billion years for H₀ = 68 km/s/Mpc — consistent with independent measurements.
The Hubble tension: Different measurement methods give slightly different H₀ values:
- CMB-based (Planck): H₀ = 67.4 ± 0.5 km/s/Mpc → t₀ ≈ 13.79 Gyr
- Distance ladder: H₀ = 73.0 ± 1.0 km/s/Mpc → t₀ ≈ 12.84 Gyr
This ~5σ discrepancy between local and early-universe measurements is one of the biggest unsolved problems in cosmology. It may indicate new physics (dark energy evolving over time, additional light particles, etc.) or systematic measurement errors.
For context:
- Solar System age: ~4.57 billion years
- First stars formed: ~200–400 million years after Big Bang
- Milky Way formation: ~1 billion years after Big Bang
- Oldest observed galaxies: ~500 million years after Big Bang (z ≈ 10–14)