The expanding universe

About a hundred years ago, astronomers measuring distant galaxies found something nobody expected. Nearly all of them are moving away from us. And the further away a galaxy is, the faster it is going.

This does not mean we are at the centre of anything. Picture a ball of dough full of raisins, rising in the oven. As the dough swells, every raisin moves away from every other raisin. Each one, if it could look, would see all the others leaving. The galaxies are the raisins, and space is the dough.

Space itself is stretching, and carrying the galaxies apart.

If everything is moving apart now, it was closer together before. Follow that back far enough and you reach a time, 13.8 billion years ago, when everything we can see was packed together, unimaginably hot and dense. The universe has been spreading out and cooling ever since. That beginning is called the Big Bang.

The observation. The light of a galaxy, spread into a spectrum, carries dark lines at known wavelengths. In nearly every galaxy beyond our near neighbours, the lines sit at longer, redder wavelengths than they should. This is redshift. In the 1920s Georges Lemaître and Edwin Hubble showed that the redshift grows in step with distance: a galaxy twice as far away is receding twice as fast.

The rate is the Hubble constant. It is about 70 km/s for every megaparsec, which is about 21 km/s for every million light years. A galaxy 100 million light years away is receding at about 2,100 km/s.

What is stretching. The galaxies are not flying through space away from a point. The space between them is growing, and light crossing it is stretched along with it. Light that set out when the universe was half its present scale arrives with its wavelengths doubled.

Three things follow.

• There is no centre and no edge to the expansion. Seen from any galaxy, all the others recede in the same way.
• Things held together do not expand. Atoms, people, planets, the Solar System and whole galaxies are bound by forces far stronger than the stretching. Even our Local Group holds together: Andromeda is approaching us. Only the gaps between groups and clusters of galaxies grow.
• Very distant galaxies recede faster than light. This breaks no rule. Nothing can move through space faster than light, but the rule puts no limit on how fast space itself can grow.

Running it backwards. A universe that is expanding was once denser and hotter. The Big Bang theory is the account of how that hot, dense state expanded and cooled into what we see. It makes predictions, and three have been checked.

The oldest light. For its first 380,000 years the universe was so hot that atoms could not hold together, and light could not travel far through the glowing fog. When it cooled to about 3,000 K, atoms formed, the fog cleared, and the light was set free. That light is still arriving from every direction, stretched about 1,100 times into microwaves. It was predicted in 1948 and found by accident in 1964. Its temperature today is 2.725 K, which is about −270 °C.

The first elements. In its first few minutes the whole universe was hot enough for nuclear fusion. The theory says this should have left about three quarters hydrogen and one quarter helium by mass, with a trace of lithium. The oldest gas clouds measured have that mix.

A changing past. Looking far away is looking back in time. Distant galaxies are smaller, younger and less orderly than nearby ones. The most distant confirmed so far, found with the Webb telescope, are seen as they were less than 300 million years after the beginning.

The age. The pattern of slightly warmer and cooler patches in the oldest light, mapped by the Planck spacecraft, gives an age of 13.8 billion years, to within about 1 per cent.

How far we can see. The oldest light has travelled for 13.8 billion years. The matter that sent it has been carried away by the expansion ever since, and is now about 46 billion light years from us. That distance, in every direction, is the limit of the observable universe. Nobody knows how much lies beyond it, or whether the whole is finite.

What the theory does not say. It does not say the universe exploded into empty space: there was no space outside it. It does not describe the very first instant, where known physics fails. And it does not say what, if anything, came before.

An open problem. The expansion rate can be measured in two ways. Stepping outwards through distances to galaxies gives about 73 km/s per megaparsec. Working it out from the oldest light gives about 67. Each measurement claims an accuracy of 1 or 2 per cent, so they should not differ this much. Either one of them hides a mistake that nobody has found, or something is missing from the theory.

The Hubble tension. The expansion rate today can be reached by two routes that share almost nothing, and they give different answers. This level sets out what each route measures, how far apart they are, and what has been tried.

The quantity. For galaxies that are not too far away, speed of recession $v$ and distance $d$ are tied by

$$v = H_0\, d$$

and $H_0$ is the Hubble constant, in km/s for every megaparsec. Its inverse is a time. Worked out here, $1/H_0$ is 14.0 billion years for $H_0 = 70$, 13.4 billion for 73 and 14.5 billion for 67.4. The true age of the universe is not simply $1/H_0$, because the expansion has not kept one speed, but the comparison shows what is at stake: a few units in $H_0$ is a billion years in the timescale.

The direct route. Measure distances to galaxies and set them against their speeds. This is the distance ladder: parallax fixes the true brightness of Cepheids, Cepheids fix it for Type Ia supernovae, and the supernovae reach far enough out for the expansion to dominate. The SH0ES team’s 2022 result, from Cepheids in the host galaxies of 42 supernovae, is

$$H_0 = 73.04 \pm 1.04\ \text{km/s/Mpc}$$

The route from the oldest light. Before the universe turned clear, sound waves ran through the hot plasma. The distance such a wave could have covered by the time the light was set free is the sound horizon, $r_s$, and it left a preferred size for the warm and cool patches in the oldest light. What is measured is the angle that size covers on the sky:

$$\theta_* = \frac{r_s}{D_M}$$

where $D_M$ is the distance the light has crossed since. Planck measured this angle to 0.03 per cent: $100\,\theta_* = 1.0411 \pm 0.0003$, which is 0.60 degrees when worked out here. The standard model of cosmology gives $r_s$ from the physics of the plasma, so the angle gives $D_M$, and $D_M$ depends on how fast the universe has expanded since. Within the standard model the answer is

$$H_0 = 67.4 \pm 0.5\ \text{km/s/Mpc}$$

This is a prediction for today’s rate from the state of the universe at 380,000 years. It is only as good as the model that carries it across 13.8 billion years.

The size of the gap. The two differ by 5.6 km/s/Mpc, which is 8 per cent of the lower figure, and about five times the combined uncertainty. The SH0ES paper puts it at 5 sigma. Its authors tried about 70 variations of their analysis and found none that closes the gap.

Other measurements. Several other methods have been brought in to break the tie.

Method	Year	$H_0$ (km/s/Mpc)
Cepheids and supernovae (SH0ES)	2022	73.04 ± 1.04
Time delays in six lensed quasars (H0LiCOW)	2020	73.3, +1.7 −1.8
Brightest red giants and supernovae (Freedman and others)	2019	69.8 ± 0.8 ± 1.7
Brightest red giants, Hubble and Webb together (Freedman and others)	2024	70.39 ± 1.22 ± 1.33 ± 0.70
One neutron star merger, by gravitational waves	2017	70.0, +12.0 −8.0
Galaxy clustering with the sound horizon (DESI)	2024	68.52 ± 0.62
The oldest light with the standard model (Planck)	2018	67.4 ± 0.5

Where more than one uncertainty is given, the first is statistical and the second systematic. The third in the 2024 figure is the scatter among the supernovae. The pattern is not tidy. Methods that lean on the sound horizon give 67 to 69. Cepheids and lensed quasars give 73. The red giant method, which replaces Cepheids with a different kind of star but keeps the supernovae, lands in between, and its authors say their results need no new physics. The gravitational-wave measurement uses no ladder at all, but one event is too few to decide anything.

Is it a mistake in the Cepheids? The most often suggested fault was crowding: in a distant galaxy a Cepheid’s light is blended with its neighbours’, which could make it seem brighter and nearer. The Webb telescope has much sharper sight than Hubble in the infrared. In 2024 the SH0ES team reported Webb measurements of more than 1,000 Cepheids, found no significant difference from Hubble’s, and ruled out crowding as the cause at 8.2 sigma.

Is it new physics? If both measurements are right, the model that joins them is incomplete. One much-studied idea is early dark energy: an extra ingredient that mattered briefly before the universe turned clear and then faded. It would have made $r_s$ smaller. With a smaller $r_s$ and the same measured angle, $D_M$ is smaller too, and the $H_0$ inferred from the oldest light rises towards the direct value. A 2021 review surveyed this and many other proposals and concluded that none makes a strong case for being far better than the rest.

Where it stands. Three possibilities remain open: an error in the ladder that nobody has found, an error in the model used to read the oldest light, or several small errors at once. More Webb data on all three kinds of star, and more neutron star mergers, are the measurements most likely to settle it.

On this site. The 3D view places galaxies using $H_0 = 70$, between the two camps. Had it used 73 every galaxy on the map would sit 4 per cent nearer, and with 67.4 it would sit 4 per cent further away. The shape of the web would be the same.