## At what speed is the universe expanding? Is it faster or slower than the speed of light?

The premise of the question is confused. The expansion of spacetime is not measured in the same units as the speed of light-the two are simply in different sets of units:- The speed of light is measured in units of velocity, which are m/s in conventional units.
- The expansion of the universe is measured by the Hubble parameter, which has units of 1/time. Astronomers typically quote the Hubble parameter today (and many incorrectly call it the Hubble "constant", but it is not constant), and give it in units of ~70 km/s/Mpc. km and Mpc are both units of length, so this really has units of 1/time.

People keep perpetuating this quote of the universe "expanding faster than the speed of light", but it doesn't make sense to compare those two quantities. It would be an interesting historical exercise to track down the origin of this quote.

The most meaning I can attribute to this quote is as follows. Remember in Hubble's law that apparent recession velocity is proportional to distance between two objects (this gets modified for cosmological distances). At any given time in the universe, you can find a distance (c/H) where the apparent recession velocity is the speed of light. Beyond that distance, objects appear to recede faster than the speed of light. But remember, apparent recession velocity is not a real physical velocity!

Question: At what speed is the universe expanding? Is it faster or slower than the speed of light?

The rate of expansion of the universe is an estimated 70 km/s per Mega-parsec. A Mega-parsec is a unit of distance equivalent to nearly 3,000,000 light-years. This means that every parsec equates to 3.3 light years. This rate of expansion is not a speed, it's the speed of expansion per distance, so it cannot be compared to, say, the speed of light. This means that the universe will expand 70 km/s for every 3,000,000 light-years that the universe has. Now, does this mean that the universe is boundless? The answer is yes, technically.

We can say that two objects distanced by a mega-parsec such as our galaxy (Milky Way) and our neighboring galaxy (Andromeda) would be further diverted at a rate of 70 km/s due to the expansion rate of the universe. Interestingly enough, this does not take a toll on the distance between the two galaxies. This is due to the fact that (because of gravity, these two objects attract each other) the Milky Way and Andromeda are approaching each other at approximately 300 km/s. In about 4 billion years, these two will collide and generate a massive cosmic explosion. But then again, don't get uneasy about it because if you're reading this, you'll be long dead before that takes place.

Nothing in the observable universe is moving away from us at or greater than the speed of light with the expansion of space, but the current understanding is that the tiny bit of space that expanded to become what is now the observable universe was a very small part of what formed at the Big Bang event. It then seems likely that there are parts of this vast space that are moving away from us at greater than the speed of light. Anything in the parts of space that are moving away from us faster than the speed of light are impossible to observe, and that makes this idea hypothetical but still constant with what we know about the part of the universe that we can see.

If the theory of cosmic inflation is even roughly correct, Inflation (cosmology) , there was an incredibly brief time right after this universe got started during which the expansion rate was much greater than the speed of light, but this expansion rate did not continue.

Very simply, the expansion of space and the speed at which something travels in space are two very different things.

The law that states that the speed of light is the very limit of anything travelling within space does not apply to space itself.

As a quick experiment, take a rubber band (cut so that it is a single strand). Make a few marks on it at varying distances with a marker.

Now, stretch.

The distance between marks increases, but they occupy the very same spot on the rubber band as when it was unstretched. In effect, space is not travelling so much as expanding. Each point in space remains in place, even while all points are becoming more distant.

Kinda mind-blowing, isn't it?

Technically, anything within space can only move from point to point in space at or below the speed of light.

Currently, we are certain that we live in a universe that is expanding at an increasing rate. As you read this, the universe expands at about 70 kilometers per second per megaparsec. This means that a galaxy 1 megaparsec away from us is receding at about 70 km/s, another galaxy 2 megaparsecs away from us is receding at 140 km/s, and so on. This is Hubble's law. Following the same logic, one could do the math to compute how far a galaxy has to be in order to move away at the speed of light. It turns out, galaxies 4300 megaparsecs away from us recede faster than light. This distance defines the "Hubble sphere", an imaginary sphere centered at us, outside which everything recedes faster than the speed of light. Note that, since the universe expands at an accelerated rate, the Hubble sphere increases its radius as time goes by.

Can we see light coming from galaxies outside the Hubble sphere? Receiving light from a source moving faster than light might seem odd, but this is actually possible. Imagine a galaxy outside the Hubble sphere, which emits a light pulse towards Earth. The pulse tries to makes its way to us, but it is "dragged" away from Earth by a region of space receding faster than light. It looks like we will never receive this pulse -- but wait a sec! As the universe expands, the Hubble sphere gets bigger, too. Now, if the rate at which the Hubble sphere expands is larger than the net velocity at which the photon recedes from us, the pulse will eventually pass from a superluminal region into a region receding from us slower than the speed of light. Take a look at this video, which transforms these words into a cool animation. Of course, as long as the pulse is traveling a region receding from us at a velocity smaller than the speed of light, it will eventually reach us. The conclusion is that we still can observe galaxies receding faster than light! Put another way, the Hubble sphere is not the limit of our observable universe.

How can we tell the universe is expanding faster than the speed of light in the first place? The wavelength of a light pulse traveling the universe is stretched as space expands, so the light gets redder. (That is, its wavelength increases.) This so-called cosmological redshift is measured by astronomers, so distant galaxies can be labeled by their redshift. The higher redshift of a galaxy, the faster it is receding from us. For any plausible model of our expanding universe, there exists a relatively simple conversion to translate redshift into recessional velocity. Not surprising by now, some of the galaxies we have observed exhibit redshifts resulting in superluminal recessional velocities!

Finally, one should note that, in practice, a receding galaxy may "disappear" from our observations due to cosmological redshift. Light coming from the galaxy gets redder and redder, leaving the detectability range of our instrument (our eyes or even a radio telescope). In addition, the time between successive pulses will increase so much that the galaxy will fade out until it vanishes.

When we say the universe expands, we mean that all distances in the universe become larger with time. Moreover, they all become larger at the same rate, everywhere in the universe. We can measure this rate of expansion of space by asking ourselves: "How long will it take until all distances become twice as long?".

The answer turns out to be a bit complicated. However, if we make some simplifying assumptions, most importantly that a parameter called the Hubble parameter is constant and will remain constant forever, we can get the following answer:

At the current rate of expansion, distances in the universe will become twice as long in approximately 9 billion years.

The universe itself will become 8 times as large, because it's 3-dimensional, and each dimension will become 2 times as large. [math]2^3=8[/math].

Notice that this means the farther away a galaxy is from us, the faster it would seem to move. Why? Let's see:

- A galaxy that is 1 million light years from us now will be 2 million light years from us in 9 billion years. So it would seem to move 1 million light years during that time.
- Another galaxy, that is now 2 million light years from us, will be 4 million light years from us in 9 billion years. So it would seem to move 2 million light years during that same time.
- Yet another galaxy, that is now 4 million light years from us, will be 8 million light years from us in 9 billion years. So it would seem to move 4 million light years during the same amount of time as the other two!

This observation, that farther away galaxies move faster from us, is called Hubble's law.

Of course, in the simple examples I gave above I didn't take into account that the galaxies are, in fact, already moving. However, their speeds at such close distances are small enough that it wouldn't matter.

What about the relation to the speed of light? Well, all the galaxies that currently less that roughly 14 billion light years from us all move slower than light with respect to us.

However, Hubble's law says that galaxies farther away move faster, so galaxies that are currently more than 14 billion light years from us move faster than light with respect to us.

Is there a contradiction with relativity here? No, because nothing is actually moving faster than light. There's a "loophole" here that comes from the fact that speed is something that you measure relative to space, but in this case space itself is expanding, so speeds are no longer meaningful.

It's like standing on a moving sidewalk (usually found at airports). You can be perfectly still, and not move at all with respect to the moving sidewalk, but the sidewalk itself is still moving.

In conclusion: Space is expanding at a constant rate, not a speed. Things in space, like galaxies, move because space itself is expanding. Their speed relative to us is proportional to their distance from us. So if they're far enough (namely more than 14 billion light years), they move faster than light. They move at that speed whether they want to or not, because space itself is moving.

(For anyone interested in how I arrived at 9 billion years, and knows some cosmology: I solved the equation [math]\dot{a}/a=H[/math] where [math]a[/math] is the cosmological scale factor and [math]H[/math] is the Hubble parameter. Assuming that [math]H[/math] is constant, the solution is [math]a=e^{Ht}=2^{Ht/\log 2}[/math]. This means that [math]a[/math] doubles itself after a time [math]t=\log 2/H[/math], which evaluates to roughly 9 billion years.)