Expert: Courtney Seligman - 10/27/2009

Question
QUESTION: Hi Courtney! Thank you for volunteering!!! Here is my question:

Given that the expansion rate of the universe is 74.2 ±3.6 kilometers/second/megaparsec, and that the radius of the universe is 14 Gpc (given my very simplistic math abilities), I estimate that the expansion rate of the outer edge of the observable universe would be 10,388,000 km/sec. Isn't faster than the speed of light (at 300,000km/sec)? How can this be?

Bruce

ANSWER: The problem is your units (and a probable decimal place error). The "observable" Universe is 13.7 billion light years in radius, not 13.7 billion parsecs. Dividing by 3.26 light years per parsec yields 4 Gpc for the radius, not 13.7. Multiplying by 74.2 km/sec/Mpc yields 297000 km/sec, which is essentially the same as the speed of light. So the numbers come out "right".

This is of course not an accident. The size of the "observable" Universe is defined as the distance at which the expansion velocity would be equal to the speed of light; so if the arithmetic is done correctly, the radius (in Mpc) multiplied by the Hubble constant (in km/sec/Mpc) always comes out equal to the speed of light.

The actual size of the Universe, however, is many times larger than that. It's just that regions which lie beyond the "observable" limit can't be observed, because as light travels from there to here, the expansion of the space through which it is traveling carries the light away from us, despite its velocity in our direction.

---------- FOLLOW-UP ----------

QUESTION: This page also says the same thing:

http://en.wikipedia.org/wiki/Observable_universe

The age of the Universe is about 13.7 billion years, but due to the expansion of space we are now observing objects that are now considerably farther away than a static 13.7 billion light-years distance. The edge of the observable universe is now located about 46.5 billion light-years away

Bruce


Answer
It is correct that the objects we now see as they were 13.7 billion years ago are now much farther away. BUT THEY ARE NO LONGER PART OF THE OBSERVABLE UNIVERSE, and how fast they are now moving away from us is irrelevant, since we can no longer see them. We can see them as they were when they were at a distance at which the universal expansion rate between us and them was close to the speed of light; but now that they are much farther away, the space between us and them is expanding at more than three times the speed of light (any given Mpc only expands at 75 km/sec, but there are a lot more Mpc between us and them now than there used to be), so their light can no longer reach us.

As an example, suppose something is now half of 13.7 Gly away, moving away at half the speed of light. As time passes, the amount of space between here and there will increase, and as the object's distance increases, so will its speed. It isn't really speeding up -- in fact, it isn't really moving away from us at all, in the normal sense of the phrase. But the empty space between us and it is expanding at a roughly constant rate, and the more empty space there is, the faster the object will seem to move away from us. At some point it will be 13.7 Gly away, moving away from us at nearly the speed of light. At that point, it would still appear more or less as it was when the light by which we see it left it. Soon afterward, the object would be more than 13.7 Gly away, and the empty space between it and us would have a total expansion rate greater than the speed of light; so it would have moved beyond the observable part of the Universe, into the unobservable part.

An odd result of this is that although the Universe is getting larger, the part of it that we can see is getting smaller. Eventually, everything which is now more than about a hundred million light years away from us will be too far away, and 'moving' away from us too fast for us to see it, and the only things left in the observable Universe will be those galaxies close enough to us that their local gravity can overcome the overall expansion.