# The Greatest Story Ever Told -- 04 -- The Expanding Universe

Ever since I was a child I have had this instinctive urge for expansion and growth. To me, the function and duty of a quality human being is the sincere and honest development of one's potential. -Bruce Lee

It isn't only our heros that expand and grow; the Universe does that, too! In the first three parts of our series, we talked about inflation, its end, and the hot big bang. But during all of this time, the Universe has been expanding.

This is probably the most confusing aspect of cosmology, so tread slowly through this. First off, it is space itself that is expanding. It doesn't make sense to ask "what's it expanding into?" Because space is like the surface of an infinitely stretchy balloon: it can get bigger or smaller, but it doesn't require anything external to itself.

Now, one of the biggest thing that we learn from General Relativity when we apply it to cosmology is how space expands, and what happens to the Universe as a result. In fact, it turns out that the only thing that governs the expansion of a flat Universe (like ours) is the Universe's energy density, and that's it.

Well, during inflation, the energy density of the Universe is a constant, which means the expansion rate (which is fast) is also constant. This means the Universe expands exponentially, like so.

The way this works is that after a short amount of time (for inflation, the time is something like 10-20 or 10-30 seconds), the size of the Universe doubles. After another one of those "doubling times", the Universe is double that new size, or 4 times the original size. If you can go for 100 doubling times (10-18 or 10-28 seconds in our two examples), the Universe will now be 2100 times its original size. It is in this fashion that we can get an arbitrarily large Universe in a fraction of a second, and that's what inflation gives us.

Come now to the end of inflation, where the entire Universe may be the size of your thumb, or it may be a bajillion (roughly) times the size of our Universe right now. The actual, physical size of our Universe at that time doesn't really matter. Why not? Because the part of it that becomes the entire observable Universe -- about 100 billion light-years across today -- was only about the size of your thumb at the moment the big bang began.

But when inflation ends and (what I call) the Big Bang began, everything changes. The expansion rate was still the same, and the energy density is still incredibly large, but now the Universe's energy is in the form of matter and radiation. When the Universe continues expanding now, the energy density drops, because you've got the same amount of stuff, but the volume it occupies increases! This means the energy density goes down, and hence, so does the expansion rate!

So the Universe inflates, and the expansion is very fast and constant. When inflation ends, matter and radiation fills a small region of this space (the region that becomes our observable Universe), and the expansion -- although still very fast -- is now slowing down. The Universe is therefore cooling as it's expanding, and despite being filled with all the possible fundamental particles that can exist at these incredible energies, will not stay that way for long.

The first thing the Universe needs to do? Figure out a way to create more matter than anti-matter, because at the very beginning, there's about a billion times more of both matter and antimatter than there is of either one today. That's the next chapter in our story, so come back for it!

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OK, so I'll bite and be the sacrificial lamb:

When the Universe continues expanding now, the energy density drops, because you've got the same amount of stuff, but the volume it occupies increases! This means the energy density goes down, and hence, so does the expansion rate!

So why do we see the expansion speeding up?

By NewEnglandBob (not verified) on 08 Feb 2010 #permalink

Am curious how the universe is 100 billion light years across but only 13 billion years old. I have had this explained to me a few times, but the explanation never seems to stick in my head.

The problem with modern science is that it ignores an element of the "universe" Consciousness. If Consciousness is a part of the "Universe" just like gravity or heat, if left out. All of the mathematical models would be invalidated. Maybe Consciousness is in the 4th dimension where time and space is the same thin? *shrugs* I don't know. I am just an Artist. ^_^ I just know how to make great paintings ^_^

It's a strength, not a problem that modern science doesn't concern itself with questions that have no empirical basis. (And please, no quantum observer responses -- that's not what guerra was referring to.) Such speculation is best left to the artists. :-)

Ethan:

I've noticed that cone shape image, (in a number of variations) showing the expansion of the universe, used several times in a number of you posts. I would like to know how the expasion would differ (if at all) based on the other all 3 shapes the universe could potentially have: Euclidian Space (zero curvature), Elliptical Space(positive curvature) and Hyperbolic Space (negative curvature).

While special relativity constrains objects in the universe from moving faster than the speed of light with respect to each other, there is no such theoretical constraint when space itself is expanding. It is thus possible for two very distant objects to be moving away from each other at a speed greater than the speed of light (meaning that one cannot be observed from the other). The size of the observable universe could thus be smaller than the entire universe.

This was a clip from wikipedia, under the 3rd hyperlink ethan posted ("...most confusing aspect...").

I've really been enjoying this series. Thanks for greatly increasing this layman's knowledge of the early universe.

Why does the inflation end?

By Lotharloo (not verified) on 09 Feb 2010 #permalink

what does the edge, or boundary, of the inflated region look like, where it merges into stuff that wasn't participating in inflation? Or is it a closed space, or is it infinite?

I accidentally posted these under Chapter 3. I repost here.

It seems to me (a layman) that there is a major problem in discussing topics like GR and the BB in a language like English. The concepts were developed mathematically, and the math assumes that we are part of the system. We cannot observe without affecting that which we observe. Our language assumes that we are outside the system, observing without affecting (See above.) Many people have been misled by trying to apply quantum concepts (and GR), expressed in English, to everyday life.

There are many parts that I do not *get* or do not *like*. I must be patient (or learn the math.

IIRC, a black hole need not have a singularity. The singularity is a point where space has infinite curvature. The defining quality of a BH is the event horizon. One could have sufficient mass to form an event horizon but not enough to form a singularity (I think.)

The formation of the singularity could be a problem with our math, and not a problem with space-time. There is so much we don't know. Exciting times.

Tom

By Sweetwater Tom (not verified) on 09 Feb 2010 #permalink

@NewEnglangBob:

So why do we see the expansion speeding up?

Because "the expansion rate goes down" does not contradict "the expansion speed goes up". Two different things!

In mathematical language, the expansion speed is the time derivative of the scale parameter (or equivalently of the curvature radius), a_dot, whereas the expansion rate is this expansion speed, divided by the scale parameter, i. e. a_dot/a (which is the Hubble constant, BTW). It's easy to show mathematically that one can have a growing a_dot, although a_dot/a is falling. Picture it this way: a is growing faster than a_dot (the size of the universe grows faster than its expansion speed), hence the ratio of the two is going down.

Or, even more mathematically: taking the time derivative of a_dot/a, we arrive at a_dotdot/a - (a_dot/a)^2. If (adot/a)^2 is high enough, this whole expression will be negative, even if a_dotdot is positive.

Sorry if I used too much math here - Ethan, can you explain it in simpler terms?

"Fabric of The Cosmos" - Brian Greene. Read it along with "The Greatest Story Ever Told", I assure you, it will blow you away!

Bjoern & NEBob,

I wrote a post about how this works back in August. The version with math is here: http://scienceblogs.com/startswithabang/2009/08/the_math_of_the_expandi…

The version without math is the first hyperlink in that post. (If I post a second link, I'll get caught in my own spam filter.)

crd2,

Are you referring to the very top image? If so, that image doesn't assume that the Universe is spherically shaped. It assumes that our location in the Universe can observe light from objects located as far away as the radius of that sphere extends, but no farther. And therefore, there is no dependence on the curvature of space.

The farther away an object is from us, the faster it appears to recede from us. The expansion rate of the Universe -- the Hubble parameter -- is 71 km/s per Mpc, which means that for an object that's even 4500 Mpc away from us (around 14 billion light years), it expands away from us faster than the speed of light. Since the expansion can exceed the speed of light (but light travel can't), we can see the light coming from objects that were once closer to us that are now beyond our reach, permanently. So even though we've had about 14 bilion years of time, the farthest object we can see is about 46 billion light years away from us, which means the "observable Universe" is about 92-93 billion light years across. Does that help?

If the energy density remains constant during inflation, then
a) where does that extra energy come from? Surely as the Universe expands whatever energy there is gets more and more spread out, so to maintain a constant density, new energy has to be coming from somewhere. Is this something to do with the gravitational field containing negative energy?

and

b) why is the Universe diluted to a near vaccuum after inflation? If the energy density remains constant, why does it drop to nearly nothing?

Also, in your last part of this series, you said the energy at the moment of the Big Bang could have been compressed into a space the size of a proton. Surely this can't be true? Inflation, which came before the Big Bang, must have made the observable universe bigger than that?

(I'm loving this series, anyway. Just a few things I'd like clearing up though :3)

I should have beer more specific when refering to the image in my post @ 5. I was refering to the last image. It shows the expanding universe as a sort of bell shape.

I'm more interested in where it all came from. As an atheist, one must believe the universe is self-created. Any thoughts on how that can be? Shakespeare wrote that nothing will come of nothing. Could he be wrong?

By morton kaplan (not verified) on 10 Feb 2010 #permalink

I'm more interested in where it all came from. As an atheist, one must believe the universe is self-created. Any thoughts on how that can be? Shakespeare wrote that nothing will come of nothing. Could he be wrong?

By morton kaplan (not verified) on 10 Feb 2010 #permalink

1) One could say that the increase in energy is exactly compensated by an increase in negative gravitational potential energy (as you already suggested). Several cosmologists propose that, AFAIK, but so far, I haven't seen a convincing calculation showing that. Further, there is the problem that in General Relativity, "gravitational potential energy" is not even well-defined (it is described by a pseudo-tensor instead of a tensor - I hope you know these terms?).

Hence explanation 2: energy is in general not conserved in General Relativity (that's the explanation I prefer, until someone shows me some convincing arguments and calculations why it should be conserved). For more details, see here:
http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

With respect to you second question: I suspect that when Ethan talked about a "near vacuum", he meant the particle density, not the energy density.

@morton kaplan: AFAIK, there are also models in which the universe never actually had a beginning, but has existed forever (e. g. Steinhardt's ekpyrotic model). I don't know if these are still consistent with the available evidence, though.

crd2: The bell shape in that last image actually has nothing to do with the curvature of the universe. The idea is that the universe at any given moment is displayed as a flat disk, sort of representing what we might see if we could stand in one place and look out at the whole universe. The changing circumference of the universe over time is what traces out the bell shape.

guerra
Let me stray off topic with you.
Clearly, consciousness is part of the universe because you and I are part of the universe.

Derek
Wiki defines: "The word empirical denotes information gained by means of observation, experience, or experiment." That seems to apply to our understanding and study of consciousness.
I personally am of the opinion that good science is a lot like art. Robert S. Laughlin (1998 Nobel Prize physics) says, "Good theoretical physics is actually more like art than engineering and is similarly difficult to summon up on demand. The physical idea precedes the mathematics, and the act of writing it down as a simple equation is like capturing a song or a poem", A different Universe pg, 89 by Robert S. Laughlin.

What is apparent versus what is real and how does it depend upon which theory you believe? Assuming a rigid Euclidean astronomical yardstick, the radius of our visible universe is 13.7 Billion light years. However, using an expanding big bang cosmological yardstick, the radius of the universe is about 50 billion light years. But which theory you believe or not (I don't accept the big bang theory) doesn't matter as long as you know which yardstick is being used.

@Thomas:

I don't accept the big bang theory

Why not?

BTW, Since you have time to write blog posts, do you also have time to continue our mail discussion again?

our universe is nothing more than what has been sucked into a black hole from another dimension.

In given time will we pop or just continue to expand to infinite space and time?

Are we inside of a black hole now? How could you measure the entropy of this "state"? If time was created @ the instant of the big bang, what is on the other end?

What if we are only on the surface (like fish in a pond) (ants on the ground) surly the big bang was incredibly loud maybe a bad "note" caused the big bang and maybe it was heard

By nate haynos (not verified) on 12 Feb 2010 #permalink

Why do I not accept the idea that the whole universe as we observe it today once fit "into a volume the size of your thumbnail.. (or).. into a volume the size of a single proton)"? I think Aristophanes needs to write another play. But seriously, I will take some time and compose a short answer as to why I remain skeptical of this fantastical scientific conclusion of the big bang theory.

My apologies Bjoern. I do owe you an email, which I will focus on before I write another word on this or any blog. My time is freeing up again. Best regards, Tom

The universe we know is believed to start from a singularity [at least something very small] from the beginning of the big bang about 13-15 billion years ago. If, as you said, 'the entire observable Universe [is] about 100 billion light-years across today', some parts of it must have been travelling at a speed faster than light. How could this be possible?

By Yew-Kwang Ng (not verified) on 23 Feb 2010 #permalink

You said, 'the entire observable Universe [is] about 100 billion light-years across today'. How could we observe something 50 billion or more light years away, a it would take no less than 50 billion years for light to travel from there to reach us, while the big bang was only about 13-15 billion years ago?

By Yew-Kwang Ng (not verified) on 23 Feb 2010 #permalink

An answer that has often been given to Question 24 above I posted earlier is that space itself is expanding. If everything in the universe is expanding, then though each specific thing cannot travel locally at a speed faster than light, things can be more than 30 billion light years apart after 15 billion years. I find this explanation not easy to comprehend. All things are close together at the time of the big bang 13-15 billion years ago, and now some thing is more than 90 billion light years from some other thing. The relative speed they become further than another is faster than the speed of light. I think this is not allowed under relativity theory.

By Yew-Kwang Ng (not verified) on 23 Feb 2010 #permalink

An answer that could be given to Question 25 above I posted earlier is that the light from those distant stars/galaxies we see now originated billions of years ago when the universe was much smaller. However, if the universe is about 93 billion light years across now, it could not be smaller than 45 billion light years across 10 billion years ago. My estimation (not perfect) is still impossible for the edge of the observable universe some 40 odd billion light years ago could be observed by us now.

By Yew-Kwang Ng (not verified) on 23 Feb 2010 #permalink

However, if the universe is about 93 billion light years across now, it could not be smaller than 45 billion light years across 10 billion years ago.

Why not?

You have already provided what (so far as I know) is the correct answer to your question - as we look further away, we see things that were within our light cone at the time billions of years ago that their light started towards us but which have been pushed out of it by the subsequent (superluminal) expansion of space, so the 'observable universe' encompasses a 'real' volume larger than 13.7 billion light years' radius; but I'm afraid I don't understand why you reject this explanation.

If the expansion rate is expanding why isnt the density expanding along with it?

The universe is expanding at a rapid rate.
CMB is a constant throughout the measured universe.
Question:
Why isn't the universe cooling as an expanding gas cools?

@Jim Long: The CMBR *is* cooling (although this has little to do with the cooling of an expanding gas) - it had a higher temperature at earlier times (there are even some measurements showing that). The CMBR is only *spatially* constant throughout the measured universe, not temporally!

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hat's right, it's an AMERICAN knife, made in CHINA. And we all know that Asians do everything better. It's probably got some ancient Chinese magic built right in. You've got

Servant of God, Bishop Fulton Sheen, once said, "There are not more than 100 people in the world who truly hate the Catholic Church, but there are millions who hate what they perceive to be the Catholic Church.

I remember watching so many of those moments. My favorite is obviously Manning to Tyree. I remember as soon as that play happened I said to my dad that would be the greatest play in Giants and Football history.

Adam Baker, 33, is facing one count each of assault with a deadly weapon and failure to return rental property, two counts of communicating threats and five counts of writing worthless checks, authorities said.

as energy dissipates all possible masses are achieved but seems arbitrary from a fixed observation point.

The way in which politicians want to mask higher costs with lower prices is to increase taxes. Some suggest taxing "Cadillac" health insurance plans.

Interesting thoughts about matter and non-matter.Is there any study available which proves that matter and non-matter were both existed in abundance when this universe started t shape up?

I see the galaxy in a different way. Maybe it didnt have a binging well you say it has a binging, yeah i will agree that every thing have a binging and ending.But the past 15, 30 70 100 bilion year ago there were darkness or maybe other planets . Or no one knows even black holse ,worm holse started it, we might say black holes have the power (gravity) to destroy a star . But the past years There were dinosaurs on earth. we dont know what creatures exist before them , we know dinosaurs. B/s we find there bond may be the bone of thing that existed before them decomposed. Dinosaurs died for men kind to live. The only thing there is a theory ,a theory is a theory if there no thing that support it.