# Stellar formation / Expansion / Education questions

1. May 17, 2013

### TigerDaveJr

Regarding the creation of the universe and the current model:

Is it assumed that the universe, at the time of creation was finite in size (or at least more finite than it is now) prior to the rapid expansion, or was the protoexistance finite in size in an infinite universe? So, did the universe AND its contents expand, or did a collection of mass within the universe expand, creating the physicality we know today?

I have seen the expansion explained like a balloon. However, if this were true, would not most mass be on the 'outside' of the balloon? Is there content in the middle of the universe, or is there a hollow center that is getting bigger as we get further from the center? I've read that asking about the center is impossible, and that the universe has infinite shape, but if that's true can we say we're expanding? Would there not be an origin point, or is that one of the problems that a physics-uneducated person like myself would be unable to grasp (re: Plato's allegory of the cave).

Can we not use red shift in order to determine the relative center of this expansion? I understand that we observe red shift based upon where we're standing, but should we not be able to calculate from all that where the overall center is? Where are we in regards to this?

Was expansion more like bread dough? Did the pre-expansion material tear? Was that tearing uneven, that left behind general emptiness in some spots and densely clumped matter in others that led to our original star nurseries?

Are galaxies considered expanding or collapsing? I've heard that there's supposed to be black holes in the center, so is this local mass "going down the drain" or is this mass being spun off from the center? Is it both? Do we consider galaxies to be generally "on par" with each other in the creation of more complex atomic structures, or do we expect each birth/nova/collapse/rebirth cycle of stellar material to continually generate more complex material, and that individually from galaxy to galaxy?

Second to last, is it possible, in the same way that we view time against the overall amazingness of deep time, that this initial universal expansion was just one bubble in an even larger sea of expanding pockets that we have yet to get close enough to see the evidence of? Not getting into dimensions, but is our universe just one in an entire "hyper-universe" of immense activity, that we can't directly "observe" in the same way that our tiny blip of existence fits in the concepts of deep time?

Finally and most importantly, where should I be aiming myself educationally in order to learn the answers to these questions, and to ask even more?

2. May 18, 2013

### Bandersnatch

Hello, TigerDaveJr. Welcome to PF!

The universe was either finite or infinite, and it still is one of those. We cannot say which one it is, but if it's finite, then it has got a very large curvature radius(~88 billion ly was the minimum estimate, iirc).
The key part to understand is that whenever you hear of the universe's expansion, it does mean the entirety of it. It's not about some matter expanding into a preexisting space, but space WITH matter and energy, expanding.

The balloon analogy is not perfect, as it creates this erroneous intuition that there is something outside(or inside) the balloon, due to the way we imagine it being a three dimensional object.
The analogy requires you to think of only the surface of the balloon as the universe.
There is no centre to a 2d surface(but there is curvature), and the expansion is still easily observable by comparing the distances between any two points on that surface at two different times.

These two pages go into more detail about the balloon analogy, its aims and limitations, all in layman's terms:
http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf (first page is blank)
http://www.phinds.com/balloonanalogy/

You should see from the above links that it is impossible to define a centre of uniformly expanding space.
You can easily define the centre of the observable universe, which is wherever you are standing.

You are taking the analogy too far. Of course the universe is not made of dough, so it does not tear like dough does. It is important to limit yourself to only what the analogy is trying to convey(i.e., the expansion of space) and not to go overboard with drawing conclusions from it.

Galaxies are stable structures, with no significant amount of mass going down the black hole or escaping.
Sure there might be some rogue star gaining enough speed from random gravitational interactions to fling itself into the intergalactic space, and there tends to be some gas falling down the black hole - mostly because it takes so long to actually get there.
But overall, there is no expansion or collapse. The expansion of space does not affect small scale structures(like galaxies), and the black holes are not the voracious vaccuum cleaners of doom that you might sometimes see in the popular media. Most stars stay in pretty much stable orbits around the galactic centre, and it's not going to change much, barring collisions with other galaxies.

All the galaxies coalesced from the same primordial gas, and the laws of physics governing them are the same, so it stands to reason that they are similar.
The difference is in the time scale. As you look farther away, you see younger galaxies, and the younger the galaxy, the less time its stars have had to go through their life cycles and produce heavier elements.
Generally the longer the universe exists, the more heavy elements it contains(in the early universe there was only hydrogen, helium and some lithium).

It's a kind of a vague and dangerously philosophical-sounding question, but I suppose it asks about the multiverse hypothesis?
As you say, it's not observable, therefore not falsifiable, which makes it an empty question really.
The first half an hour or so of this talk by Lee Smolin:
http://pirsa.org/13020146/
touches on the subject.

I'd recommend starting here:
http://www.astro.ucla.edu/~wright/cosmolog.htm
and going through either/both tutorial or/and FAQ.

Stephen Weinberg's "First three minutes" is a classic book concerning the early expansion of the universe. It's a bit dense at times, and getting somewhat old, but still worth reading.

Alan Guth's "The Inflationary Universe" talks about the birth of the idea of inflation, that is a major(if still somewhat dodgy) part of current cosmology.

Finally, understanding Relativity might be necessary. This popular treatment by Einstein himself is a good start:
http://www.gutenberg.org/files/30155/30155-pdf.pdf

You should be able to understand the ideas without any maths knowledge, but once you dig deeper into cosmology, you'll notice that it's at its heart a mathematical science, requiring you to learn higher mathematics to truly understand what's going on.
Unless you do that, you'll have to do with imperfect analogies, so if you have such an option, take calculus and algebra courses.

Finally, you might find the courses/videos on these sites relevant to your interests:
http://www.perimeterinstitute.ca/video-library (you probably want the "public lectures" section)
https://www.coursera.org/ (actual online courses; physics section covers cosmology as well)
https://www.khanacademy.org/ (not a lot on cosmology, but good for learning maths and basic physics concepts)

3. May 18, 2013

### Mordred

Along with the excellent material already mentioned I would add the following article

http://arxiv.org/abs/1304.4446

this article reviews the LCDM model which is the current concordance model. (concordance meaning the most agreed upon by the scientific community)
Although LCDM is a good fit to observational data there are other good fit models to observational evidence.
The paper I posted covers current cosmology without any of the maths so its handy for those that do not know the maths.
As pointed out however to really ubderstand what us going on you will need to understand the math involved.

An alternate analogy to the balloon analogy is to use a 3d grid coordinate. Each vertical, horizontal and z crossing forms a coordinate.
As expansion occurs none of the coordinates change nor do any of the angles between x,y or z change.
The space between x,y or z simply increases.
I always prefer the grid analogy over the balloon or raison bread analogies mainly because it can also show how curvature affects the sum of angles which relates to the universes geometry. Which also helps in understanding commoving and proper coordinates as well as light
cones.
my signature includes a link to
a handy calculator called lightcone 6.0. Thus calculator will help you in various maths involved in the expansion history of the universe past, present or future.

4. May 18, 2013

### TigerDaveJr

So, the most important part of the balloon analogy is to get away from the concept that the ballon itself is a 3d construct in 3d space and only focus on the plane expansion into an immense curvature. This makes much more sense for the sites where I'm reading the universe is flat.

So, when we're looking at the outlier clusters of material that are getting faster away from us, that is only local perspective, yes? And that, from their location, we're getting faster away from them. Aside from local cluster material (as I've read regarding blue-shifted objects) every group should be able to look at every other object and see the same thing: we're all expanding from each other. And because of this, there can't be a definable center. So as you said earlier, from personal perspective the center is ... where you happen to be at, but this isn't something like a ball or any other 3d object in that we can identify the central core, etc. If there are no definable edges, there can be no definable equidistant from all edges.

I hope that's on the right track because that really cleared up a lot of questions I had. I definitely need to get into the higher maths to see this at work. Your assistance has been invaluable - thank you.

5. May 18, 2013

### Mordred

There is no center or preferred location. Expansion occurs every where expect gravitationally bound regions equally.

Im having trouble getting the latex working from my phone on a print out history from the calculator however this thread has some print outs

Last edited: May 18, 2013
6. May 18, 2013

### marcus

Hi Mordy, here is the 10 step history that Jorrie's calculator opens with:

$${\scriptsize\begin{array}{|c|c|c|c|c|c|}\hline R_{0} (Gly) & R_{\infty} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.9&0.693&0.307\\ \hline \end{array}}$$ $${\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&S&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&D_{hor}(Gly)&V_{now} (c)&V_{then} (c) \\ \hline 0.001&1090.000&0.0004&0.0006&45.332&0.042&0.057&3.15&66.18\\ \hline 0.003&339.773&0.0025&0.0040&44.184&0.130&0.179&3.07&32.87\\ \hline 0.009&105.913&0.0153&0.0235&42.012&0.397&0.552&2.92&16.90\\ \hline 0.030&33.015&0.0902&0.1363&38.052&1.153&1.652&2.64&8.45\\ \hline 0.097&10.291&0.5223&0.7851&30.918&3.004&4.606&2.15&3.83\\ \hline 0.312&3.208&2.9777&4.3736&18.248&5.688&10.827&1.27&1.30\\ \hline 1.000&1.000&13.7872&14.3999&0.000&0.000&16.472&0.00&0.00\\ \hline 3.208&0.312&32.8849&17.1849&11.118&35.666&17.225&0.77&2.08\\ \hline 7.580&0.132&47.7251&17.2911&14.219&107.786&17.291&0.99&6.23\\ \hline 17.911&0.056&62.5981&17.2993&15.536&278.256&17.299&1.08&16.08\\ \hline 42.321&0.024&77.4737&17.2998&16.093&681.061&17.300&1.12&39.37\\ \hline 100.000&0.010&92.3494&17.2999&16.328&1632.838&17.300&1.13&94.38\\ \hline \end{array}}$$

7. May 18, 2013

### Mordred

Thanks Marcus working from a phone gets fustrating lol.

Anyways as you can see the calculator is a handy tool for seeing the expansion history.
It also has graphing capabilities as shown in the other thread. As well as a couple more row options.
Marcus has posted numerous examples of its usage on PF.
The above pinned thread "See 80 billion years into...." above has a large collection of examples
skip near the end though as there
is numerous older versions lol.

Here is a link to the main page under development. PF members such Jorrie and Marcus are fine tuning.

http://cosmocalc.wikidot.com/start

There is several links to how to use the calculator. Including a user manual, a tutorial manual and advanced info for the math usage.

Last edited: May 18, 2013
8. May 18, 2013

### marcus

Hi TigerDaveJr, your post#1 asked reasonable and clearly worded questions which to me seem kind of exemplary newcomer questions. That is one reason Bandersnatch was able to make such an excellent answer in post#2. I was impressed by its conciseness accuracy and completeness so I quoted post#2 to have for reference in the "balloon analogy" sticky thread, here:
Thanks both for this very useful exchange. IMO it's a real contribution.

Last edited: May 18, 2013
9. May 18, 2013

### Mordred

I couldn't agree more

10. May 18, 2013

### Mordred

you may find this article will be handy in regards to redshift, cosmic distance measures and expansion.

11. May 18, 2013

### Bandersnatch

It's spot on.
Once you wrap your head around it, it makes perfect sense. Have fun learning!

Oh, and thanks for the accolades, you guys.

12. May 18, 2013

### marcus

Now that TigerDave's question is well and truly answered, let me ask you about your 88 Gly figure for the lower limit of radius of curvature (in your post#2). I have the same rough impression ≈ 100 Gly.

Do you have a recent reference that you like? There seem to be a lot of 95% confidence intervals for Ωk. Presumably one wants to take the square root of the absolute value of the most negative and divide the Hubble radius R by it:
R/|Ωk|.5

I posted some links to Planck estimates of Ωk here:
I don't especially like them, just what I was able to come up with. You may have others to compare. Some of those I quoted in that post were:
==quote==

...using observations of the CMB alone:

100ΩK= −4.2+4.3-4.8 (95%; Planck+WP+highL);
100ΩK= −1.0+1.8 -1.9 (95%; Planck+lensing + WP+highL)

...by the addition of BAO data. We then find

100ΩK = −0.05+0.65-0.66 (95%; Planck+WP+highL+BAO)
100ΩK = −0.10+0.62-0.65 (95%;Planck+lensing+WP+highL+BAO)
==endquote==
This was from page 40 of http://arxiv.org/abs/1303.5076

Last edited: May 18, 2013
13. May 19, 2013

### Jorrie

How would one find the maximum likelihood value from these ranges? 100ΩK = -0.10 - 0.65 + 0.62 = -0.4?

It is obviously so close to Ω=1 that it might not matter. Putting Ω = 1.004 into LightCone yields the following minor changes from flat space:
Age: 13.7543 vs 13.7872 Gy flat
Event Hor: 16.476 vs 16.472 Gly flat
Particle Hor: 46.081 vs 46.279 Gly flat

Sorry, goofed with a zero, but have already posted; it is even closer, 100ΩK = -0.10 - 0.65 + 0.62 = -0.13
Age: 13.776 vs 13.7872 Gy flat
Event Hor: 16.473 vs 16.472 Gly flat
Particle Hor: 46.214 vs 46.279 Gly flat

Last edited: May 19, 2013
14. May 19, 2013

### marcus

What happens if we just take the central value 100Ωk = -0.1?

Then we have to divide the Hubble radius R=14.4 Gly by the square root of 0.001 which is 0.0316
so 14.4/.001^.5 = 455 Gly

Ugh

Let's not include BAO, that represents counting galaxies. Let's just base everything on observations of the Cosmic Microwave Background. Pick the best-tasting cherries. It's 1AM here. I'm off to bed. :-D

Last edited: May 19, 2013
15. May 19, 2013

### Jorrie

What I find fascinating is how a non-zero curvature would evolve over time. If I understand correctly, a non-zero 'curvature density parameter' Ωk evolves with a-2, meaning the radius of curvature Rk evolves with a-1. Using the above value for the present, Rk = 455 Gly, then at the time of the CMB, it was around 500 trillion light years and at a = 100, it will be only around 4.5 Gly. This points towards an extreme curvature (small radius) as a -> infinity.

Or do I have the relationship wrong?

16. May 19, 2013

### Bandersnatch

So I've spent a good few hours trying to track down the source I got it from, but with no luck. But even if I did, that would do us little good, as I'm pretty sure that was not the most recent of papers. It would stand to reason that the constraints on the minimum radius improved with more data from WMAP streaming in.

17. May 19, 2013

### marcus

This much I do think is right, at least the curvature does evolve with a-2. Now remember that curvature is big when the radius is small. The curvature is by definition 1/Rk2. I believe the radius of curvature evolves with a.

So in the future when a=100, the radius of curvature would be 100 times what it is today.

Rk(a=100) = 100Rk(now)

It would be good to check with George about this or some other knowledgeable person. But that's what I think is the case. There are problems with using Ωk because it expresses the curvature (a reciprocal area, or reciprocal square time) in a somewhat roundabout way in relation to today's critical density. And that reference quantity changes over time, which could mess up the simple proportionality if one wants to track the curvature over a long enough interval of time that the critical density might change significantly. I'll make a one-time use of it to get the radius of curvature just for NOW and then from thenceforth I'll just use the proportionality with the scalefactor a.

Last edited: May 19, 2013
18. May 19, 2013

### marcus

This much I do think is right, at least the curvature does evolve with a-2. Now remember that curvature is big when the radius is small. The curvature is by definition 1/Rk2. I believe the radius of curvature evolves with a.

So in the future when a=100, the radius of curvature would be 100 times what it is today.

Rk(a=100) = 100Rk(now)

It would be good to check with George about this or some other knowledgeable person. But that's what I think is the case. There are problems with using Ωk because it expresses the curvature (a reciprocal area, or reciprocal square time) in a somewhat roundabout way in relation to today's critical density. And that reference quantity changes over time, which could mess up the simple proportionality if one wants to track the curvature over a long enough interval of time that the critical density might change significantly. I'll make a one-time use of it to get the radius of curvature just for NOW and then from thenceforth I'll just use the proportionality with the scalefactor a.

19. May 19, 2013

### Jorrie

I think you are right - if not zero, curvature was much closer to zero (critical density) in the past and will evolve away from zero in the future. Since critical density was much higher in the past, it means curvature was higher in the past and will be smaller in the future. I think this is where I did the head-flip to 1/a for the radius, instead of just a. One should analyze actual densities in this case and not normalized density ratios, like Ω.

20. May 20, 2013

### marcus

Recalling a previous post with a link to Planck estimates of CURRENT Ωk:
Some of those quoted in that post were:
==quote from page 40 of http://arxiv.org/abs/1303.5076 ==
...using observations of the CMB alone:

100ΩK= −4.2+4.3-4.8 (95%; Planck+WP+highL);
100ΩK= −1.0+1.8 -1.9 (95%; Planck+lensing + WP+highL)
==endquote==

We could take the second of these and calculate the radius of curvature in two cases, the
CENTRAL VALUE for the present-day ΩK namely -0.01
and also the MOST NEGATIVE VALUE namely -0.029

and then we could calculate the radius of curvature corresponding to these two cases.

(central value) Rk= 14.4/(.01).5 = 144 billion lightyears
(most negative) Rk= 14.4/(.029).5 = 84.5597116 billion lightyears

WOW! There is Bandersnatches 88 Gly radius of curvature!
Basically we get 85 Gly and we are using March 2013 Planck report numbers so of course slightly different from whatever his 88 was based on but very likely the same type of thing. Namely some 95% confidence interval for presentday Ωk taking the MOST NEGATIVE end of the confidence interval---therefore corresponding to the most positive curvature and thus to the SHORTEST RADIUS of curvature.
In our case the confidence interval was [-0.029, 0.008] they almost all tend to be lopsided towards negative thus favoring positive curvature. this is no exception.