Expansion speed and accelleration question

[narrator]

Expansion "speed" and accelleration question

I was reading about how the OU was once the size of a grapefruit, which prompted me to think about expansion acceleration.

At the time that the OU was the size of a grapefruit, the universe had to be expanding faster than light, otherwise the OU would have been bigger than a grapefruit (Hubble et al).

Step forward some billions of years and the OU is as we now know it, with the universe expanding faster than light... and accelerating.

This led me to think that there are one of three possibilities:
1. Expansion did not accelerate for an unknown period sometime between the grapefruit and now, leaving current expansion at perhaps a little faster than it was during the grapefruit era, or
2. If it has accelerated ever since the time of the grapefruit, then either that acceleration is so miniscule as to be hundreds of decimal places, or
3. If it has accelerated ever since, and not at a miniscule rate, then the current velocity due to expansion (not from ordinary movement) has to be in the order of many many time light-speed.

Am I missing something?

 

[phinds]

At the time that the OU was the size of a grapefruit, the universe had to be expanding faster than light, otherwise the OU would have been bigger than a grapefruit (Hubble et al).

Uh ... say WHAT? I don't follow your logic at all. That statement does not seem to make sense. What am I missing about it?

Step forward some billions of years and the OU is as we now know it, with the universe expanding faster than light... and accelerating.

This led me to think that there are one of three possibilities:
1. Expansion did not accelerate for an unknown period sometime between the grapefruit and now, leaving current expansion at perhaps a little faster than it was during the grapefruit era, or
2. If it has accelerated ever since the time of the grapefruit, then either that acceleration is so miniscule as to be hundreds of decimal places, or
3. If it has accelerated ever since, and not at a miniscule rate, then the current velocity due to expansion (not from ordinary movement) has to be in the order of many many time light-speed.

Am I missing something?

Acceleration of the expansion of the U started somewhere around 6 to 8 billion years after the singularity. It was at this point that "dark energy" was able to start overcoming gravity outside of gravitationally bound systems such as galaxies.

To say that the universe is expanding FTL is somewhat misleading. What is happening is that distances are growing in all areas outside of gravitationally bound systems. The growth is nowhere FTL, BUT it is cummulative, so objects that are really far apart DO have the distances between them growing FTL, and the farther apart they are, the faster the distance between them is growing. If there are objects WAY outside of the OU (and I assume there are even though we'll never have direct evidence) then they are receding from each other at many times c

 

[narrator]

Uh ... say WHAT? I don't follow your logic at all. That statement does not seem to make sense. What am I missing about it?

If the observable universe was once the size of a grape fruit, per this http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf" ("Cosmologists sometimes state that the universe used to be the size of a grapefruit, but what they mean is that the part of the universe we can now see—our observable universe—used to be the size of a grapefruit."), then anything beyond that grapefruit has to be separating from the "observer" faster than light or it would be "observable". Have I got that right?

To say that the universe is expanding FTL is somewhat misleading. What is happening is that distances are growing in all areas outside of gravitationally bound systems. The growth is nowhere FTL, BUT it is cummulative, so objects that are really far apart DO have the distances between them growing FTL, and the farther apart they are, the faster the distance between them is growing. If there are objects WAY outside of the OU (and I assume there are even though we'll never have direct evidence) then they are receding from each other at many times c

If we talk about "expansion" in the sense that I read it here in PF, then surely it's not misleading, taking into account, as you say, the gravitationally bound systems. And going by your last sentence, my thinking in my 3rd possibility is true, or close to the truth.

Going on from that, if the expansion has therefor been accelerating for some 30 billion years, it makes me wonder at the current rate of expansion, given that it has been accelerating for that long. Even a tiny acceleration over 30 billion years would suggest that "they are receding from each other at many times c" is an understatement. Have I missed something?

 

[Omniverse]

I've been wondering about this recently.

Assuming that the Hubble constant is constant through time as well as space then the observable universe should be of a constant radius. This radius would be the distance that is expanding at the speed of light.

Note that I am assuming Euclidean rather than relativistic expansion in my "back of a stamp" calculations.

H₀ ≈ 73km/s/MPc is the Hubble constant
c ≈ 3 *10⁵km/s is the speed of light
H_r is the Hubble radius (is this the right term? I mean this to be the distance between two points such that the space between them expands at the speed of light c)

These units are not easily usable together so I'll fit them all into light years as distance.
73km/s ≈ 73/(3 *10⁵) ≈ 2.3*10^-4
1 MPc ≈ 3.26*10⁶ c (from http://en.wikipedia.org/wiki/Parsec" )
so the normalised H₀ ≈ (2.3*10^-4)/(3.26*10⁶ ≈ 7.46*10^-11 s^-1

Taking the reciprocal of this gives with light years as the units the distance that I refer to as H_r ≈ 13,397,000,000c​

I understand that taking relativity into account will change this figure a bit, but it seems to me that in my Euclidean expansion the maximum size of the visible universe is approximately 13.5Bn light years with today's currently observed value of H₀. Put simply, any photons that are emitted at this distance or greater from us will never be able to reach us because even though they are approaching us at the speed of light the distance they must travel to reach us is growing at the speed of light or greater.

The coincidence between the similarity of this calculated value and the commonly accepted value for the age of the universe is striking given that the expansion is only supposed to have been accelerating for the last 7Bn or so years.

Do any more knowledgeable members of this forum have any comments to make regarding my thoughts on this?

Now for some wild speculation. (Only keep reading for fun )

It seems to me that in a universe with varying H₀ over time there is no reason for the big bang. If H₀ were permitted to oscillate over time then H_r would be proportional to H₀ and during a period of negative H₀, conditions within the visible universe (which with contraction is limited only by time and not H_r like expansion) could quickly enter a high energy state such as is theorized to occur shortly after the time of the big bang. This would be because photons that are currently trapped on the sphere defined by H_r during an expansion would suddenly swamp the visible universe during a contraction. In addition, photons from outside the visible universe woud be highly blueshifted due to the contraction and the amount of these gamma rays and other high energy particles that would reach us would cause instant radiation death for all matter, reducing it to a particle soup.

I say "outside the visible universe" because there is no way of knowing exactly how big the universe is outside our expanding bubble of space with a radius of 13.5Bn light years and it could be infinite. The main historical argument against an infinite universe is that light would reach us from every point in the sky and the sky would be bright instead of dark, but with an expanding universe this would not be the case since photons would get trapped at the distance of H_r.

With negative H₀, the sky may indeed be bright in all directions. Expansion doesn't even need to be constant through space. There could be localised expansion and contraction, but on distance scales as small as our visible universe the constancy of H₀ through space might just be an approximation to within experimental limits.

Might make for an interesting scifi novella.

 

[phinds]

If the observable universe was once the size of a grape fruit, per this http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf" ("Cosmologists sometimes state that the universe used to be the size of a grapefruit, but what they mean is that the part of the universe we can now see—our observable universe—used to be the size of a grapefruit."), then anything beyond that grapefruit has to be separating from the "observer" faster than light or it would be "observable". Have I got that right?

AH ... I see now what you mean, and yes you are correct.


If we talk about "expansion" in the sense that I read it here in PF, then surely it's not misleading, taking into account, as you say, the gravitationally bound systems. And going by your last sentence, my thinking in my 3rd possibility is true, or close to the truth.

Going on from that, if the expansion has therefor been accelerating for some 30 billion years, it makes me wonder at the current rate of expansion, given that it has been accelerating for that long. Even a tiny acceleration over 30 billion years would suggest that "they are receding from each other at many times c" is an understatement. Have I missed something?

UH ... 30 billion years? That's going to be a tough one to prove since the U is only 13.7 Billion years old.

Things at the edge of the OU are receding at a little over c, things (again, assuming there ARE things) many trillions of light years further out are receding correspondingly faster. And farther than that, faster still. But again, nothing is actually MOVING FTL, it's just that distances are getting bigger, which is not the same thing.

 

[narrator]

UH ... 30 billion years? That's going to be a tough one to prove since the U is only 13.7 Billion years old.

Oop.. my bad.. uhh.. 6 billion, after subtracting the period before expansion..

Things at the edge of the OU are receding at a little over c, things (again, assuming there ARE things) many trillions of light years further out are receding correspondingly faster. And farther than that, faster still. But again, nothing is actually MOVING FTL, it's just that distances are getting bigger, which is not the same thing.

If thing just at or beyond the edge of our OU are only receding at a little over c, then expansion must be accelerating at such a small rate, say 10^-100 parsecs/year^2, or else over so many billions of years, the recession speed would have built up enormously.

 

[phinds]

If thing just at or beyond the edge of our OU are only receding at a little over c, then expansion must be accelerating at such a small rate, say 10^-100 parsecs/year^2, or else over so many billions of years, the recession speed would have built up enormously.

I found this most memorably expressed once by the following quote: "Even though the universe is expanding, it's still going to be hard to find a parking place". Silly, I know, but the explanation behind it was about the speed of expansion and how it is really really tiny over short distances. The example was if you magically paint a pair of parking space lines in intergalactic space, how long does it take for them to move far enough apart to accommodate another car? The answer was in the billions of years. BUT, when you add up all the local expansion over a vast distance, it increase amazingly fast (FTL, is, after all, REALLY fast)

 

[narrator]

I like that, very elegant :)

 

[marcus]

Oop.. my bad.. uhh.. 6 billion, after subtracting the period before expansion..

If thing just at or beyond the edge of our OU are only receding at a little over c, then expansion must be accelerating at such a small rate, say 10^-100 parsecs/year^2, or else over so many billions of years, the recession speed would have built up enormously.

You might like some numbers. The edge of OU corresponds roughly to redshift z=1100.
that is the redshift of the oldest light (CMB) from the farthest matter we can see. At this moment the matter is about 45.6 billion LY from us and receding at about 3.3c.

It might be fun to calculate the ACCELERATION of that distance growth. It is probably not too helpful to think of anything as moving, just as distance increasing, and at an increasingly rapid pace.

You are right that these rates are miniscule. As you suggested in your post the acceleration of distance growth is going to be numerically very tiny.

a(t) is the scale factor which is conventionally normalized so a(now) = 1

a(t) has no units. It tells proportional increase.

I will write the time derivative with prime. a'(t) is the rate a(t) is increasing. a"(t) is the acceleration. Here are some approximate figures.

a'(now) = 2.3 x 10^-18 per second

a"(now) = 3 x 10^-36 per second per second.

It will be convenient to write the present "radius of OU" in LIGHT SECONDS.

45.6 billion LY is 1.44 x 10¹⁸ light second.

Remember what a'(now) is. 2.3 x 1.44 = 3.3. That is why I say the distance to that ancient matter is increasing at rate 3.3 c. But as time goes on we see beyond that matter so perhaps I should say that the surface of last scatter (where the matter is that emitted the ancient light) is actually receding at rate 4.3 c. But I want to focus on the matter which we are seeing today and stick with that. So I say the distance to that particular matter is increasing at rate 3.3c.

Is this clear? Let me know if I need to rephrase it to make it less confusing.

Now to get the ACCELERATION of that particular distance we just need to multiply 1.44 x 3.

It is 4.3 x 10^-18 c per second.

So every second the recession speed adds a tiny increment of speed which is about
4.3 billionths of a billionth of c, the speed of light.
=====================

Maybe that is hard to picture. A billionth of c is about one foot per second. So in a billion seconds the recession speed increases 4.3 feet per second.

this is focussing on a specific fixed bunch of matter which emitted the CMB radiation which we are seeing today---that bunch of matter is NEAR the edge of our OU, but not quite at the exact limit. The limit keeps including new matter as its light gets time to reach us.
=====================

Anyway this is just a rough scratchpaper calculation to help imagine. It is not important. But it shows your intuition was right. You guessed that the acceleration would be very slow if you applied it to some definite real distance. (Like the radius of the Observable region.)

What really counts is the scalefactor a(t). That is what grows according to the Friedman equation which is the basic equation of classical cosmology. People are well advised to learn about a(t) and the Friedman equation. And not to worry too much about the radius of the Observable and whatever it is doing. Just my two cents.

If I made some dumb calculator error hopefully someone else will catch it, but i think this is OK.

 

[Drakkith]

Wow, thanks for the number crunching marcus! I had no idea things were receding from us at over 3x the speed of light near the edge of the observable universe.

 

[narrator]

Marcus, that was a perfectly wonderful explanation, just on the edge of my own OU of understanding. And for the first time since coming to this forum, I now understand the calculations. The numbers you have so eloquently put to it all have greatly expanded my understanding.

Are you a teacher? If not, you ought to be.

It is probably not too helpful to think of anything as moving, just as distance increasing, and at an increasingly rapid pace.

A misconception I had some months back, yes. But always worth the clarification.

Is this clear? Let me know if I need to rephrase it to make it less confusing.

All very clear. Thank you.

Maybe that is hard to picture. A billionth of c is about one foot per second. So in a billion seconds the recession speed increases 4.3 feet per second.

I must admit, such numbers are hard to picture, but when you put it that way, it's very helpful.

---that bunch of matter is NEAR the edge of our OU, but not quite at the exact limit. The limit keeps including new matter as its light gets time to reach us.

That's something I didn't know. I was under the misconception that expansion meant we would be slowly losing objects from our OU.

Where do we get some of the numbers you've quoted? I can't imagine we could distinguish redshift with enough accuracy without the help of theory and other calculations to give the observations such precision.

Edit: Page bookmarked

 

[marcus]

Wow, thanks for the number crunching marcus! I had no idea things were receding from us at over 3x the speed of light near the edge of the observable universe.

Drakkith, I do solemnly recommend to you this real simple little calculator that Siobhan Morgan posted for her astronomy students
just google "cosmos calculator" or use the "morgan" link in my signature.

At the beginning of each session you prime it by putting in .27, .73, 71
for "matter density" "cosmological constant" and "Hubble" rate.
There are three boxes over at the side and you put those numbers in (to get standard results).

Then you put in whatever redshift. Like 1100 for the microwave Background.

I like it because it is totally simple. It tells you distance now and distance then (when the light was emitted) and it also tells you recession rate now, and also what it was then.
And it tells you what the Hubble parameter was back then too.

So it tells you just what you need to get a mental picture. And does not distract you with a lot of other technical stuff.

You may have been using a more technical cosmology calculator, like Ned Wright's. With more features and jargon. Darn! I meant say "professional terminology". Wright's calculator also has more decimal places. Both come in handy.

 

[Drakkith]

You may have been using a more technical cosmology calculator, like Ned Wright's. With more features and jargon. Darn! I meant say "professional terminology". Wright's calculator also has more decimal places. Both come in handy.

Actually I don't think I've gotten around to hitting up one of those calculators. My interests lead me to many places, sometimes I don't get too deep into one thing before moving on. At least until I come back to it lol.