The universe is expanding. Every galaxy is receding from every other. Let us understand why, and how we know.
Imagine a loaf of raisin bread baking in the oven. As the bread rises, all the raisins move away from each other, not because the raisins themselves are moving through the bread, but because the bread itself is stretching. The universe works the same way. Space itself is expanding, and every galaxy is being carried away from every other galaxy.
Edwin Hubble discovered in 1929 that the farther a galaxy is from us, the faster it is moving away. This single observation changed everything we thought we knew about the universe.
Hubble noticed a pattern. Galaxies twice as far away move twice as fast. Galaxies ten times farther move ten times faster. There is a perfect, clean relationship between distance and speed. We now call this Hubble's Law.
Think of it like this: if you are standing in the center of the rising bread, every raisin that is 1 centimeter away moves at a certain speed. A raisin 2 centimeters away moves twice that speed. The bread does not have a center, but the math works out the same from any raisin.
If everything is moving apart now, then in the past, everything must have been closer together. Wind the clock back far enough and all of space, time, matter, and energy was packed into a single point. That moment of birth, roughly 13.8 billion years ago, is what we call the Big Bang.
Hubble's Law gives us a way to estimate the age of the universe. If you know how fast things are flying apart, you can work backward to figure out when they all started together.
The number H0, called the Hubble constant, tells us the current rate of expansion. Measuring it precisely is one of the most active debates in modern cosmology.
How did Hubble know galaxies were moving away? He used light. When a source of sound moves away from you, the pitch drops. The same happens with light: when a galaxy moves away, its light stretches to longer, redder wavelengths. Astronomers call this redshift. The faster the galaxy moves, the more redshifted its light appears.
Redshift is the universe's speedometer. By measuring how much a galaxy's light has been stretched, we can calculate exactly how fast it is receding from us.
A galaxy is 100 million light-years away. Another galaxy is 300 million light-years away. Compared to the nearer galaxy, how fast is the distant galaxy moving away?
Hubble's Law is not just a curiosity. It is the foundation of modern cosmology. It tells us the universe had a beginning, that it is not static or eternal, and that there is structure to space itself. Every discovery since, from dark energy to the cosmic microwave background, builds on this one observation made nearly a century ago.
Hubble's Law states that the recession velocity of a galaxy is proportional to its proper distance from the observer:
The current accepted value of H0 is approximately 67-73 km/s/Mpc, though a tension between different measurement methods (the Hubble Tension) remains unresolved. For every megaparsec (about 3.26 million light-years) of distance, a galaxy recedes roughly 70 km/s faster.
One Megaparsec (Mpc) = 3.086 x 10^22 meters = 3.26 million light-years. These are the natural units of extragalactic astronomy.
The observational basis of Hubble's Law is spectroscopic redshift. For non-relativistic recession velocities (v much less than c), the redshift z is defined as:
Hubble measured absorption line spectra of galaxies and compared the observed wavelengths against laboratory standards. The systematic blueshift toward shorter wavelengths meant approach; redshift toward longer wavelengths meant recession. Almost every galaxy he observed was redshifted.
Add galaxies with measured redshift and distance. Fit the Hubble constant from your data.
Measuring galaxy distances is the hardest part. We cannot use a single method for all scales. Instead, astronomers use a chain of methods, each calibrating the next:
| Rung | Method | Range | Notes |
|---|---|---|---|
| 1 | Parallax | up to ~10 kpc | Geometric, most direct |
| 2 | Cepheid Variables | up to ~30 Mpc | Period-luminosity relation |
| 3 | Type Ia Supernovae | up to ~1000 Mpc | "Standard candles" |
| 4 | Hubble's Law itself | cosmological | Assumes H0 is known |
Each rung introduces its own systematic uncertainties, which is part of why the measured value of H0 still has debate around it depending on which rungs you trust.
Galaxies do not follow Hubble's Law exactly. They also have peculiar velocities, local motions due to gravitational interactions with neighboring galaxies and clusters. At small distances (a few Mpc), these peculiar motions can dominate over the Hubble flow. This is why Hubble's Law only becomes reliable at distances of roughly 10 Mpc and beyond, where the cosmological expansion overwhelms local dynamics.
Our own Milky Way and the Andromeda galaxy are gravitationally bound and will eventually merge. Their relative motion is actually a blueshift, opposite to Hubble's Law at local scales.
A rough estimate of the age of the universe follows from a simple dimensional argument. If galaxies have been moving at their current speeds since the beginning (ignoring acceleration or deceleration), then the time since everything was together is approximately:
For H0 = 70 km/s/Mpc, converting units gives roughly 14 billion years. The actual age (13.8 billion years) is close but not identical, because the expansion rate has not been constant. Early deceleration due to gravity and later acceleration due to dark energy modify the exact calculation.
Hubble's Law is not a postulate, it is a consequence of Einstein's field equations applied to a homogeneous, isotropic universe. The FLRW metric encodes this geometry:
The proper physical distance between two comoving observers at comoving separation r0 is:
Differentiating with respect to time gives the recession velocity:
Substituting the FLRW metric into Einstein's equations gives the Friedmann equations governing the evolution of a(t):
Define the critical density at which the universe is spatially flat (k=0):
Define density parameters for each component:
The first Friedmann equation becomes the closure relation:
The Hubble parameter evolves with redshift as:
The equation of state w = p/(ρc²) determines how each component dilutes as the universe expands. The energy density scales as:
This gives us the three distinct eras of cosmic evolution: radiation domination (a ~ t^1/2), matter domination (a ~ t^2/3), and dark energy domination (a ~ exp(Ht)), the de Sitter phase we are currently entering.
The most pressing unresolved problem in modern cosmology is the Hubble Tension: two independent classes of measurement give inconsistent values of H0 at the 4-5 sigma level.
| Method | H0 (km/s/Mpc) | Uncertainty | Anchor |
|---|---|---|---|
| CMB (Planck 2018) | 67.4 | ±0.5 | Early universe |
| BAO + BBN | 67.6 | ±1.1 | Early universe |
| Cepheids + SNe Ia (SH0ES) | 73.0 | ±1.0 | Late universe |
| TRGB (CCHP) | 69.8 | ±1.7 | Late universe |
| Gravitational Waves | 70.0 | ±12 | Independent |
The probability that this discrepancy is a statistical fluctuation is less than one in a hundred thousand. Either we have systematic errors we have not found, or there is genuinely new physics beyond the standard LCDM model.
Early dark energy models introduce a component that modifies the sound horizon before recombination, effectively shifting the CMB-derived H0 upward. Interacting dark energy and modified gravity theories alter late-time expansion. Some physicists suspect unaccounted systematics in Cepheid calibrations. The JWST has partially complicated the picture by confirming many of the Hubble Space Telescope calibrations, increasing confidence in the high H0 measurement.
This tension may be the first empirical signal pointing beyond LCDM cosmology, the Standard Model of cosmology that has otherwise described observations with extraordinary precision.
Numerically integrate the Friedmann equation for configurable cosmological parameters and observe how H(t) and a(t) evolve.
On the background of Hubble expansion, small density perturbations grow via gravitational instability. The evolution of a density contrast delta = delta_rho / rho in the matter-dominated era follows:
The growing mode solution in matter domination is simply delta ~ a(t), giving the linear growth factor D+(a). Structure formation is therefore directly sensitive to the expansion history encoded in H(t).
Peculiar velocities induced by structure growth distort galaxy redshift surveys in a specific pattern described by the parameter beta = f/b, where b is the linear bias. Measuring this simultaneously with the BAO standard ruler gives a combined constraint on H(z)*r_s and f*sigma_8, allowing cosmological parameter extraction independent of the distance ladder.
This is why future surveys like DESI, Euclid, and the Rubin Observatory are expected to significantly sharpen the Hubble Tension. They constrain H0 through geometric probes entirely independent of Cepheid calibrations.
The comoving Hubble horizon r_H = c/(aH) sets the scale of causal contact. During inflation, this scale shrinks (modes exit the horizon). During decelerated expansion, it grows (modes re-enter). The angular scale of the first CMB acoustic peak corresponds to the sound horizon at recombination projected across the distance to the last scattering surface, giving a geometric constraint on the product H0 * d_A, where d_A is the angular diameter distance.