Wing V · the map roomRoom I of I
Inv. no. V.1 · the Hubble flow
The expanding universe
In 1929 Edwin Hubble put the distances of a couple of dozen galaxies next to the redshifts of their light, and found the further a galaxy is, the faster it moves away. Not because we are in the middle of anything. The galaxies are hardly moving at all: the space between them is growing, everywhere at once, and every galaxy sees all the others recede in the same way. Below, the stretch, the law it makes, and what it does to light that has been on its way for billions of years.
Everyone is in the middle
Fig. I. Galaxies fixed to a grid that stretches. The arrows: how fast each one recedes, seen from the ringed galaxy. Click another and stand there.
- Space
- Galaxy A
- Galaxy B
- A and B
Every galaxy stays at its own spot on the grid; only the grid grows. Then a galaxy twice as far away has twice as much growing space between it and you, so it recedes twice as fast, and the arrows get longer in proportion to the distance. Click any other galaxy and the picture is the same from there: everything flies away from you, in every direction, in proportion. That is why the expansion has no centre. It is not an explosion into empty space with us near the middle; there is no edge and no outside, only distances growing.
The galaxies themselves do not grow. Gravity holds a galaxy together far more strongly than the expansion pulls it apart, and the same goes for the Milky Way's neighbours: Andromeda is coming towards us at about 110 km/s and will merge with us in some four to five billion years. Hubble's law is about the large scale, where galaxies are too far apart to hold each other back. You do not expand, nor does the Earth's orbit, nor the Milky Way.
The law
Fig. II. The Hubble diagram, live: the galaxies of Fig. I within 150 Mpc of where you stand. Dashed, Hubble's own slope of 1929.
Put the galaxies of the field above on a diagram, distance across, speed up, and they fall on a straight line through zero. Stand on another galaxy and you get the same line: the slope is the Hubble constant, H₀, the same for every observer. The points do not sit exactly on it, because every galaxy also moves a little on its own, a few hundred km/s, pulled about by its neighbours. Close by that own motion wins, which is why Andromeda can come towards us; further out the expansion wins, and the line shows.
Hubble's own line, dashed, was about seven times too steep: he measured about 500 km/s per megaparsec. His speeds were fine, his distances too small. They rested on Cepheids, pulsating stars whose rhythm gives away how bright they really are, a rule Henrietta Leavitt had found in 1912; it later turned out that there are two kinds of Cepheid, and Walter Baade's correction of 1952 doubled the size of the universe at a stroke. The slope came down step by step to the 67 to 73 of today. Georges Lemaître had derived the same law from Einstein's equations in 1927, two years before Hubble, in a Belgian journal hardly anyone outside Belgium read; since 2018 the International Astronomical Union recommends calling it the Hubble–Lemaître law.
Looking back
Fig. III. The light of a galaxy on its way to us, from the moment it left until tonight. Its waves stretch with space; the faint line is the light's distance from us as time goes on.
- When the light left, the universe was
- The light has travelled
- Distance when it left
- Distance now
- Receding now at
- Universe then
- Blue light (450 nm) arrives at
- On the way
The redshift of distant light is not a Doppler shift, though up close it looks like one. While the light is on its way, the space it crosses stretches, and its waves stretch with it: 1 + z is how many times larger the universe is now than when the light left. Light from z = 1 left when everything was half as far apart; the afterglow of the Big Bang, at z ≈ 1,100, left when the universe was a thousandth of its present size, as the orange-white glow of a gas at about 3,000 degrees, and arrives as microwaves.
"How far away" then has several answers. The light from a galaxy at z = 1 has been travelling for about 8 billion years, but it is not 8 billion light years away: when the light left it was nearer, about 5.5 billion, and today it is about 11 billion, receding at three quarters of the speed of light. Past about 14.5 billion light years, the Hubble distance c/H₀, reached at z ≈ 1.5, galaxies recede faster than light. That is allowed: nothing moves through space faster than light, but the space between can grow faster. Strangest of all, light that left from beyond z ≈ 1.6 at first got further from us, swept back by the stretching, before it could start to gain ground. Pick GN-z11 and watch the faint line.
Who worked it out
Where it already matters
The age of the universe. Run the expansion backwards and everything was once together. 1/H₀ is about 14.5 billion years; with the slowing by gravity and the speeding up by dark energy taken into account it comes to 13.8 billion. Hubble's 500 gave about 2 billion, younger than the oldest rocks geologists were already dating, a contradiction that only went away when his distances were corrected.
The Hubble tension. Measured from the afterglow of the Big Bang, with the standard model of the universe, H₀ comes out at 67.4 ± 0.5 (Planck, 2018). Measured nearby, with Cepheids and exploding stars, at 73.0 ± 1.0 (SH0ES, 2022). The difference is far larger than either error. Other ladders of distances land in between, and astronomers are still arguing whether it is a hidden mistake or something missing from the model.
A galaxy "13 billion light years away". In the news that is nearly always the light travel time. The galaxy itself is now some 30 billion light years from us; when its light left, it was only a few billion.
Why the Webb telescope sees in infrared. The ultraviolet and blue light of the first galaxies has been stretched ten to fifteen times on its way, deep into the infrared. A telescope built for visible light would see nothing there; Webb was built cold, far from the Earth, to catch it.