Hubble's Law Simulator: Redshift, Distance & the Expanding Universe

simulator intermediate ~10 min
Loading simulation...
v = 7,000 km/s — z ≈ 0.023

A galaxy at 100 Mpc with H₀ = 70 km/s/Mpc recedes at 7,000 km/s, corresponding to a redshift z ≈ 0.023 — comfortably in the linear Hubble-flow regime.

Formula

v = H₀ × d (Hubble's law)
z = v / c (low-redshift approximation)
t_H = 1 / H₀ ≈ 9.78 × 10⁹ / H₀ years

The Expanding Universe

In 1929 Edwin Hubble combined Vesto Slipher's galaxy redshift measurements with his own distance estimates to reveal a stunning pattern: galaxies recede from us at velocities proportional to their distance. This simple linear relation, v = H₀d, demonstrated that the universe is expanding — one of the most profound discoveries in the history of science. The Hubble constant H₀ encodes the current expansion rate and, inversely, provides a first estimate of the universe's age.

Redshift as a Cosmic Ruler

Cosmological redshift stretches the wavelength of photons traveling through expanding space. For nearby galaxies the relationship is straightforward: z ≈ v/c. At higher redshifts the full general-relativistic formula is needed, integrating the expansion history through the Friedmann equations. Type Ia supernovae, baryon acoustic oscillations, and the CMB all serve as standard rulers and candles calibrated against Hubble's law to map the expansion history.

The Hubble Tension

Modern cosmology faces an unresolved puzzle: local measurements of H₀ using Cepheid-calibrated supernovae consistently yield ~73 km/s/Mpc, while the Planck satellite's analysis of the CMB gives ~67 km/s/Mpc. This 4–5σ discrepancy, known as the Hubble tension, has survived multiple independent cross-checks and may point to new physics — early dark energy, additional relativistic species, or modified gravity — beyond the standard ΛCDM model.

From Hubble Flow to Cosmic Fate

At small scales peculiar velocities (gravitational motions within clusters) can mask the Hubble flow, but beyond ~100 Mpc the expansion dominates. The ultimate fate of the universe depends on the balance between matter (Ωm) and dark energy (ΩΛ): our observed values suggest eternal accelerated expansion, with galaxies beyond the Local Group eventually disappearing beyond our cosmic horizon.

FAQ

What is Hubble's law?

Hubble's law states that the recession velocity of a galaxy is proportional to its distance: v = H₀ × d. Discovered by Edwin Hubble in 1929, it was the first observational evidence that the universe is expanding. The proportionality constant H₀ (the Hubble constant) has units of km/s/Mpc.

What is the current value of the Hubble constant?

Measurements disagree: the Planck CMB analysis gives H₀ ≈ 67.4 km/s/Mpc, while local distance-ladder measurements (Cepheids + Type Ia supernovae) give H₀ ≈ 73 km/s/Mpc. This 'Hubble tension' may hint at new physics beyond the standard ΛCDM model.

Can galaxies recede faster than light?

Yes. At sufficient distances the expansion rate exceeds c, but this does not violate special relativity because it is the metric of space itself expanding, not objects moving through space. Photons from such galaxies are permanently redshifted beyond our observable horizon.

How does Hubble's law relate to the age of the universe?

The Hubble time t_H = 1/H₀ gives a rough estimate of the universe's age (~14 Gyr for H₀ = 70). The actual age depends on the expansion history, modified by matter and dark energy densities — the ΛCDM model yields 13.8 billion years.

Sources

Embed

<iframe src="https://homo-deus.com/lab/cosmology/hubble-expansion/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub