I’ve seen a lot of confusion over what precisely the term ‘observable universe’ refers to. This post is an attempt to remedy that. Crossposted from my personal website. 

In 1929, Edwin Hubble discovered that the universe is expanding. He observed that light emitted from distant celestial objects was redder than expected, due to the downward shift in frequency as their light receded from Earth. And the further away the objects were, the proportionately greater their redshift. Since objects were getting further apart from each other, figures like Lemaître and Friedmann reasoned that there must have been some point in the past at which the whole universe was compressed into a single point.

Embarrassingly, linear extrapolation implied an age of the universe of 1-2 billion years, shorter than the known age of the oldest rocks on Earth. One of the difficulties is that expansion flipped from slowing down to speeding up after several billion years, and this requires complex observations of supernovae to account for. In any case, astronomers eventually measured the age of the universe at about 13.8 billion years. This implies three tempting definitions for the observable universe — that part of the whole universe which we can theoretically see — only one of which is correct.

Universe age in light-years: You would be forgiven for thinking that the observable universe is a sphere with a radius of 13.8 billion light-years centred on the Earth, since that’s how long light has had to reach us. However, this assumes the universe isn’t expanding or contracting.

The Hubble radius: Hubble found that the distance to a given galaxy was proportional to its recessional velocity, with a constant of proportionality now called the Hubble constant H. This implies there is a sphere past which everything is travelling away from us faster than the speed of light. This is known as the Hubble sphere, and it has a radius of around 14.4 billion light-years.

You may worry that this faster-than-light travel violates Einstein’s theory of relativity, which says that nothing can travel faster than light. However, what relativity says is that matter within space can’t travel faster than light, but nothing about how fast space itself can travel.

The Hubble sphere isn’t the observable universe either. The radius of the Hubble sphere will be given by c/H, where c is the speed of light. And the Hubble constant is decreasing: the relative velocities of celestial objects are (on average) growing more slowly than the distances between them. Therefore the Hubble sphere is expanding. If the Hubble sphere expands fast enough, light leaving an extremely distant object can get ‘caught’ and drop from the faster-than-light region outside the sphere to the slower-than-light region inside. Once this light is within the Hubble sphere, it can make its way to Earth (this is explained well in this video). If you work out their present distance from us, it turns out that all of the photons we receive from the first five billion years of the universe’s existence were all caught by the Hubble sphere. These objects were, are, and always will be travelling away from us faster than the speed of light!

The particle horizon: The full extent of the observable universe is bounded by the particle horizon, which is the region from which light has had time to reach us since the beginning of the universe, taking into account its expansion. The particle horizon has a radius of 46.5 billion light-years, so the observable universe is 93 billion light-years across.

The famous cosmic microwave background is at the particle horizon, and its light has taken 13.8 billion years to reach us (the fact that it consists of microwaves is an extreme version of redshifting). In the jargon, the proper distance (the actual distance not taking into account the expansion of the universe) is 46.5 billion light-years but the comoving distance (taking account of expansion) is 13.8 billion years.

The particle horizon limits how far in distance we can observe, while the Hubble sphere limits how far back in time we can observe. We could never see objects outside the Hubble sphere as they are now, no matter how long we waited. Moreover, just as light can get caught in the Hubble sphere, the expansion of space can push light out of it. Every second, 20,000 stars become newly unobservable from Earth. In a few billion years, the observable universe will consist of only our Local Group of a few dozen galaxies. Future astronomers would gaze upon a barren universe.

Thanks to Gytis Daujotas for reading a draft of this post.