Hubble Tension — Two Ages of the Universe

Early-universe H₀ (Planck CMB)

H₀_early (km/s/Mpc) 67.4

Late-universe H₀ (local ladder)

H₀_late (km/s/Mpc) 73.0

Matter density (shared)

Ω_m 0.315

Cosmic time 13.79 Gyr

Live readouts

Age · CMB branch

13.79 Gyr

Age · local branch

12.79 Gyr

Age gap (the "tension")

1.00 Gyr (7.3%)

H₀ discrepancy significance*

5.0σ

*Illustrative: assumes σ≈0.5 (CMB) and σ≈1.0 (local ladder) km/s/Mpc, the rough real-world published uncertainties.

How it works

Both branches are flat matter + dark-energy (ΛCDM) universes with the same closed-form solution to the Friedmann equation (radiation ignored — negligible after the first ~50,000 years):

a(t) = (Ωm/ΩΛ)^(1/3) · sinh^(2/3)( (3/2)√ΩΛ H₀ t )

Age t₀ (at a=1):
t₀ = 2 / (3 H₀ √ΩΛ) · asinh( √(ΩΛ/Ωm) )   with ΩΛ = 1 − Ωm

The two branches share Ωm but use different H₀: the "early" value comes from fitting the acoustic-peak pattern in the cosmic microwave background (Planck satellite, H₀≈67.4), the "late" value from the local distance ladder — Cepheid variables calibrating Type Ia supernovae (SH0ES, H₀≈73.0). A larger H₀ means the universe is expanding faster today, which — for the same expansion history — means it needed less time to reach a=1. That is exactly why the local-ladder branch is younger.

H₀_early / H₀_late sliders — move either measurement within its real published range; the two galaxy lattices rescale live using the exact a(t) formula above.
Ω_m slider — shared matter density; raising it slows the transition into dark-energy-dominated (accelerating) expansion and shifts both ages.
Play expansion — animates cosmic time from a≈0 to today for both universes at once, so the growing age gap between the two lattices is visible directly, not just as a number.

This ~5σ mismatch between early- and late-universe H₀ measurements is a real, unresolved problem in modern cosmology called the Hubble tension — it is either new physics beyond ΛCDM, or an unidentified systematic error in one of the two measurement chains.

t = 13.79 Gyr

Early (CMB) branch Late (local) branch

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