# Expansion of the universe

Last Edited By Krjb Donovan
Last Updated: Mar 11, 2014 07:55 PM GMT

## Question

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

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 ----------

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

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.

## Question

QUESTION: Hello,

I am wondering, since the expansion of the universe is accelerating, has there been any detailed calculations of the universe's size, esp. from the beginning and up to the present? Is it known how big the universe is? I know it came into being something like 13.7 billion years ago, but can we backtrack from its current size and find out how big it was, say, when the Earth was formed 4.6 bilion years ago?

Just wondering. Thanks! - Tue Sorensen

You ask some very thoughtful questions! I hope to give you a little more "food for thought".

First of all, from your questions, I'm pretty sure you're familiar with the "standard model" of the Big Bang expanding universe. That is, the universe started as a hot "singularity", went through an inflationary period (exponential expansion to account for the observed homogeneity and isotropy of the universe), and is currently accelerating under the influence of dark energy. Current projections indicate that the Big Bang happened some 13.7 billion years ago. All this is probably pretty familiar to you. Now to get to the answers to your questions, the best I can.

When you ask how big the current universe is, the best answer I can give is that 13.7 billion light years seems to be the limit of the observable universe. In other words, if we believe that the origin of space-time itself (this is the "Bang" - it wasn't a REAL Bang, because the universe wasn't expanding into anything - all space-time started an expansion into NOTHING), then light cannot cannot have travelled more than 13.7 billion light years). But astronomers are reluctant to talk about the "size of the universe", since we're not sure if the universe is bounded or unbounded (space is definitely curved in 4 or more dimensions), and we don't have a meter-stick to measure the universe. Even if we had a meter-stick long enough (or some other indirect measure that we may develop), that measuring device would be warped by the compression of space-time as we get to the early universe (at great distance, which is equivalent to saying back in time). So the only way we could get a measure of the universe is from an observer outside the universe (not a easy feat!).

So we cannot say how big the current universe actually is (unless you can say that the observable universe IS the universe by definition!), so we can't say how big it was when the earth was formed. I suppose one could say that IF people were around with telescopes when the earth was formed, the observable universe's size would be 13.7 - 4.6 billion light years.

Now, let me add some additional "food for thought". The standard Big Bang model, although "accepted" by the great majority of astronomers, has some major problems. For one, the "expansion", if it really exists, may be quite different than generally accepted if the red-shift of light has another explanation. The very eminent astronomer Halton Arp has devoted the latter part of his career to proving this, and has done a remarkable job. I refer you to one of his very readable books, entitled "Seeing Red", which explains some of his ideas (and observational proofs). Or just Google "Halton Arp".

I also refer you to another book by three very outstanding astrophysicists / cosmologists. Its title is "A Different Approach to Cosmology", by F. Hoyle, G. Burbidge, and J. V. Narlikar. They propose a Quasi-static (oscillating) universe, which had no Big Bang. Again, they make some very convincing arguments.

So just because the majority believes in the magic 13.7 Billion year ago "Bang", please keep an open mind. Cosmology has more questions than answers, but only by continuing to ask the questions, can we work towards the "correct" answer.

Cheers,

Prof. James Gort

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QUESTION: Thank you very much; you were very helpful! I will definitely look into Halton Arp's ideas. And yes I do know a bit about the standard model (entirely in non-mathematical terms, though). I have some ideas of my own as well, but I do believe there was a Big Bang.

I guess my question really relates to the rate of expansion of the universe. If the expansion is accelerating, is it possible to calculate the rate at which the universe expanded in the past? Clearly, if the expansion accelerates, it hasn't always been expanding with the speed of light?? Or can it expand faster than that?

Can I trouble you with yet another (slightly related) question? I have just read Charles Stross' science fiction novel "Singularity Sky", and he mentions "lightcones" a lot in relation to (also faster-than-light) space travel. Am I right in assuming that the "lightcone" thing relates to the observable universe...? Can you explain a bit about why this involves a "cone-shaped" approach?

Take your time; there's no hurry.

Thanks, - Tue

Hello Tue,

For your first question, yes, the rate of expansion can be calculated. And I guarantee you - the answer will be wrong! There's just too much uncertainty. IF the universe is accelerating (still a big IF in my opinion), then the universe's size at the moment of earth's formation will have been a little less than we estimated (using a linear extrapolation). If the expansion accelerates, it is unlikely that the speed of recession of any galaxy (relative to another) will exceed the speed of light. That will require an infinite energy or a revisit to the Theory of Relativity. Neither is impossible, but I would judge them unlikely. So that means that IF we are in an accelerating phase, we MUST then enter a static or even a decelerating phase. The mechanics of these changes are not understood. Which is one reason that I said the current understanding of cosmology may need major work.

Going back to the original reason which made people think the universe is accelerating - a standard "candle" - the Type 1a supernova - appeared too dim, as they were observed in galaxies which we thought were "X" distance due to their redshift (the velocity-distance relation). Because they were dimmer than expected, they were calculated to be at "Y" (greater than "X") distance. Which means the universe accelerated! Pretty weak evidence (since there could have been many other reasons for the discrepancy) - not just in my opinion, but in the opinion of Arp, Hoyle, Burbidge, Narlikar, and others.

A final point about the rate of expansion. Since the main "candle" used to determine how much the velocity-distance relation differs from linear is the Type 1a supernova, it is necessary to get many observations at various distances to estimate a rate of change (acceleration). Since supernova are very rare events, and one much catch them at their maximum light, it is difficult to get many reliable observations. This adds to the uncertainty.

Your light cone question is easier. The light cone is just a picture in 4 dimensions (space is pictured as a 2-dimensional plane). Time is the vertical axis. Since a photon travels in both space and time (it takes a finite amount of time for a photon to move through space), the cone traces out the path of a photon (or particle travelling at the speed of light). If we talk about events in the past, that's negative time (below the space plane). Future events are in positive time (above the space plane). The light cone is just a convenient way to picture movement in space-time, especially as velocities approach light speed.

If one moves very little in space but much time has passed, that means we're going up on the z-axis (time) pretty rapidly, so we're inside the light cone. All real particles (having mass) travel inside the light cone. Photons travel ON the light cone. If you can visualize anything travelling faster than light (again, this violates Relativity), that particle would be OUTSIDE the light cone (it would travel much space in very little time). Some people think that the cone itself is a barrier for particles (it takes an infinite energy to cross it), but IF it could be crossed, particles could travel faster than light (outside the light cone). Curiously, the most successful quantum theory yet developed (Quantum Electrodynamics or QED) predicts that some "individual" photons DO travel faster than light. Some travel slower. Some travel in non-straight lines. But when you add them all up, it APPEARS that a beam of light travels at "c" in a straight line. For more on this, refer to "Q.E.D. - The Strange Story of Light and Matter" by Richard Feynman (1965 Nobel Prize winner, who co-developed Q.E.D.).

Cheers,

Prof. James Gort