# At what speed does our universe expand?

Conceivably it expands with the speed of light. I do not know, but curious, if there is an answer. At what velocity, does our universe expand?

• +1 because this is a FAQ, and having it on physics.SE is valuable. – user4552 Oct 14 '14 at 3:52

The rate of expansion of the universe (the fact that all objects are receding from each other and more so if they're farther away from each other) is given by the Hubble constant $H_0= 69.32 ± 0.80 (km/s)/Mpc$ 1

Check out this plot from Wikipedia On the y axis you have the velocity with which the object is receding from us and on the x axis the current distance in a common astrophysical unit called Megaparsec (parallax of one arc-second $1\text{pc} \approx 3.26$ light yrs).

Edit:

the discrepancy circled in blue is due to the galaxies having additional internal motions on top of their receding due to expansion. The galaxies measured there are (as the label says) part of the virgo cluster. The internal motion will induce a Doppler shift that will influence the overall redshift of the galaxy

1: According 20th Dec 2012 the Hubble constant, as measured by NASA's Wilkinson Microwave Anisotropy Probe (WMAP)

• The Hubble constant. Ok! I found a more accurate value for it $$H_0 \approx (72 \pm 8) \ \frac{\rm km}{\rm s \cdot Mpc}$$ – Stephan Schielke Aug 11 '11 at 12:13
• well 68 is within 1$\sigma$ of 72. – luksen Aug 11 '11 at 12:18
• As far as i can see it is absolutly not clear. This speed is just the current speed and changes by time. Constant may be a bad word for it. It should be called Hubble parameter. – Stephan Schielke Aug 11 '11 at 12:23
• @Stephan Schielke: The Hubble constant is not a speed at all. It doesn't have units of speed. The basic answer to your question is that there is no answer to your question. Space doesn't have a speed at which it expands. More info here: physicsforums.com/showthread.php?t=508610 – user4552 Aug 11 '11 at 16:19
• @Ben Crowell: Thx. I understood that it is rather a rate and you can not speak of the speed because it is the space itself which is expanding. I love physics even if I am not a physicist :-) – Stephan Schielke Aug 11 '11 at 19:22

The recessional velocity is given by Hubble's Law and it's proportional to the proper distance from the observer to the object (galaxy or other distant object):

$$v=H_0 D$$

where $H_0$ is Hubble's constant.

As you can see, the recessional velocity beyond a certain distance, known as the Hubble distance, can be much greater than the speed of light (in vacuum). This does not violate the relativity because the recession is not a movement through the space, it's the expansion of the space itself, between the objects.

For more details check the Wikipedia article: http://en.wikipedia.org/wiki/Hubble%27s_law

• Yes. And that implies the important part of the question, is how big is the universe? How many Hubble distances is it? Is the stuff beyond our spacetime horizon similar, i.e. can we simply extrapolate from what we can see, or could there be interesting variation beyond the horizon. – Omega Centauri Aug 11 '11 at 15:54
• @OmegaCentauri: I believe that question is covered [here]:[physics.stackexchange.com/questions/26613/… – Argus May 30 '12 at 5:45
• The term of “constant” seems not appropriate. I would rather talk of a function of space-time. The term of “law of Hubble - Lemaître” seems more appropriate. – dan Jun 3 at 9:02

Perhaps it should be pointed out here that there is no such thing as "the expansion speed of the universe". The universe does not expand at a single speed. Instead the observed expansion speed depends on the distance, as given by the Hubble constant. That constant is 72 km/sec per Mpc (1 pc is 3.25 lightyears).

What Hubble tells us is that "the expansion speed rises 72 km/sec for every 3.25 million lightyear separation". Two galaxies that are separated by a distance X, measured in megaparsecs, will move apart at a speed of 72X km/sec. For example, if we look at a galaxy that's 100 Mpc (325 Mly) away, we will see it moving away from us at a speed of 7200 km/sec.

This also means that there is no center to this expansion. No part of the universe is standing still, with everything else moving away from it. Instead, everything moves away from everything else.

At what speed does our universe expand?

This question doesn't make sense in the form in which it was posed. To see why, let's start by thinking about how we know the universe is expanding.

The expansion of the universe was originally discovered by Lemaître and Hubble, who found that the redshifts of galaxies were proportional to their distances from us. To keep things simple, let's start by thinking about how this would be interpreted if we didn't know about relativity, so that velocity and distance can be defined as we expect in Newtonian mechanics. A redshift of, say, 0.037% indicates that a galaxy is moving away from us at almost exactly 0.037% of the speed of light. Hubble's observation therefore implies v=Hd, where v is the relative velocity of two galaxies, H is a number that is the same for all galaxies, and d is the distance between the two galaxies. All intergalactic distances are increasing by the same scaling factor in any given interval of time. This is exactly what happens, for example, when a piece of metal expands because it has been heated. When a piece of metal expands, we can't describe its overall expansion using a velocity in units of meters per second. A velocity can only be defined if we first specify which two atoms in the metal we're talking about. The velocity will be different if we pick a different pair of atoms. For similar reasons, it doesn't make sense to ask for "the" velocity of expansion of the universe. There is not one velocity but many.

Now suppose we fix our attention on two specific galaxies. Can they be receding from one another at a speed greater than c? This question requires relativity. General relativity does not have a uniquely defined way of talking about the velocity of galaxy A relative to galaxy B if they are at cosmological distances from one another. If we like, we can verbally describe the situation by saying that both galaxies are at rest, but the space between them is expanding. If we like, we can use certain measures of distance and time (see https://www.physicsforums.com/threads/how-are-time-and-distance-measured-in-cosmology.506990/ ) and verbally describe A and B as moving relative to one another at a rate found by taking the change in distance divided by the change in time. In fact, general relativity allows us to assign absolutely any value we like to A's velocity relative to B; it simply isn't a well-defined thing.

Conceivably it expands with the speed of light.

Since it doesn't make sense to assign a velocity to cosmological expansion, it doesn't make sense to worry about whether such a velocity is greater than c. Because relative velocities of distant objects aren't well defined in general relativity, there is no way to extend special relativity's prohibition on v>c to distant objects in general relativity. The prohibition is a local one. Locally, general relativity is the same as special relativity.

You may sometimes see statements that cosmological inflation caused the universe to expand faster than c, or that the edge of the observable universe occurs at the place where the Hubble law gives a velocity equal to c. The first statement is incorrect because the expansion of the universe can't be measured with a single velocity. The second statement is at best an oversimplification because relative velocities of distant objects are not well defined in general relativity. For one fairly natural definition of velocity, there are galaxies we observe that are now and always have been receding from us at a velocity greater than c.[Lineweaver]

[This is a copy of a FAQ entry at physicsforums.com, which I wrote with suggestions and comments from other physicsforums members.]