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Sime99
2008-Sep-19, 07:46 PM
Iíve been trying to visualize the transition between the universe being opaque and transparent with the release of the cosmic microwave background radiation which is consistent with my (admittedly very limited) understanding of the nature of the observed universe.

This then raised further questions and implications about the size and shape of the universe. Iíd like to go through my train of thought to see where Iím right or wrong in my assumptions and conclusions I draw, Iíve probably dropped in a few bad mistakes in my reasoning along the way.

Iíve tried to work my way up from a simple model and then incorporate accepted ideas to move to the next stage. I know itís dangerous to over generalize from the simple to the more complicated but if I donít write this down it is going to drive me crazy. This is the first bit of my reasoning and Iíll try and add to this after some responses unless Iím way off, which is a distinct possibility. Anyway here goes

Assumptions: static, finite, homogeneous, 3d spherical universe
At the point of transition an observer inside the universe can either be
a) right in the middle or,
b) not in the middle e.g. a half radius distance from the centre to the edge

In both cases the edge of the visible universe expands at the speed of light in all directions around the observer as the photons 1 light second away take 1 second to reach him, 2 light secs take 2 seconds etc. In case (a) there is a uniform blueshift of the light towards the observer as the gravitational effects on the photons are focused towards the centre. In case (b) the light from the centre going towards the observer is redshifted because of the stronger gravity there and blueshifted coming from the edge, heading towards the middle.

If instead of being static the universe is expanding and the CMBR is uniform from our position (as it appears to be) this would imply that either
a) we are at the centre of an expanding finite spherical universe,
b) the universe is infinite (or at least really, really big with us being relatively close to the centre),
c) the universe is finite but has a higher dimensional structure like the 3-torus or a hypersphere or
d) the universe has got a really weird structure that just makes it look the way it does

in order to balance out the gravitational effects on the photons.

Ignoring (a) and (d) because of their unlikelihood, am I correct in assuming that the gravitational effects balance out in (b) because, to paraphrase, its turtles all the way down, up, back, forward, left and right? And the effects balance in (c) because the gravitational effects of a source of gravity wrap around the universe back towards the source? And that the assumptions about (b) and (c) are the same as assuming that the universe is isotropic throughout, not just in the visible universe?

Cheers for having a look.

Sime.

Cougar
2008-Sep-19, 08:06 PM
Iíve been trying to visualize...

Welcome to the board, Sime99.

Speedfreek has a pretty good visualizable explanation/model in this thread (http://www.bautforum.com/questions-answers/76392-how-can-you-model-visualize-expanding-universe-2.html).

Sime99
2008-Sep-19, 10:50 PM
Thanks for the welcome.

I 'get' the whole universe expanding universially (as it were) thing. It was more taking that, the evenness of the CMBR and stuff like "the universe is shaped like a doughnut, but in four dimentions" and trying to combine their descriptions in a way that didn't make my brains fall out. They all pop up individually in a lot of popular science and astronomy things I listen to or read but I haven't seen anything which puts them together as they seem to have implications for each other, and wanted to make sure my mental picture wasn't too far off the mark. There's probably some low level OCD involved too.

Mabye I should quit my PhD and start an astrophysics course...

speedfreek
2008-Sep-19, 11:48 PM
How might the CMBR and the shape of the universe be connected? Rather than me launching straight into one of my long winded descriptions, have a look at these links.

From The Shape of Space (http://www.etsu.edu/physics/etsuobs/starprty/120598bg/startit.htm) - this page covers your question: Empirical Detection of the Topology of the Universe (http://www.etsu.edu/physics/etsuobs/starprty/120598bg/section7.htm)

And the closest we have to an answer so far:

Extending the WMAP Bound on the Size of the Universe (http://arxiv.org/abs/astro-ph/0604616) - PDF (http://arxiv.org/pdf/astro-ph/0604616v1)

Have a look at those, and then feel free to ask more questions! :)

BigDon
2008-Sep-20, 12:16 AM
I have a question, from your link Speed.

I don't understand the phrase used to describe some of the "flat universe" examples. That is: "In this model, the universe has Euclidean geometry, zero curvature, and will expand forever (but just barely)."

and at this level of science, is there a mathematical definition of "forever"?

( I was told once that anything past three trillion years is for all intents and purposes "forever" as far as present day humans are concerned. :) )

Neverfly
2008-Sep-20, 12:30 AM
( I was told once that anything past three trillion years is for all intents and purposes "forever" as far as present day humans are concerned. :) )

Not if you read Frasers posted article about the end of the Universe, or study Hawking Radiation vigorously:p

speedfreek
2008-Sep-20, 12:56 AM
Well, a positively curved universe is closed, and the expansion would slow to a halt and then it would contract. A negatively curved universe is open, and would continue to expand forever.

A flat universe is also open and expands forever, but expands at an ever decreasing rate (assuming no dark energy) and never quite stops expanding completely. As time tends towards infinity, expansion tends towards zero.

Sime99
2008-Sep-20, 03:06 AM
Thanks for the links Speed.

I had seen the first page before, it was one of the things that had got me thinking along the lines I had been.

I could follow what they were doing in the paper (except for the maths) and it confirmed what I had been thinking which is probably a good thing. Its nice to see physicists and philosophers being "uncomfortable with the notion of a universe that is infinite in extent". It gives me the willies.

I've probably just missed it somewhere but was I correct in assuming that the CMBR surface of last scattering receeds at the speed of light (ignoring the expansion of the universe)?

And that an infinite universe or a 3-torus shape (or something like it) is required to maintain homogeneity and isotropy or it would show up as a blue or redshifted CMBR (or there would be a hole in the CMBR)? I guess it would depend on the matter density at the time of emission how visible this would be.

There's something thats bugging me about the expanding universe and the intersections of the surface of last scattering but I can't quite put my finger on it yet.

It's late, I'm tired, I'm meant to be writing a (CompSci) paper of my own and I'm having trouble spelling words like 'meant'. Not a good time to start thinking about Relativity.

speedfreek
2008-Sep-20, 12:53 PM
I've probably just missed it somewhere but was I correct in assuming that the CMBR surface of last scattering receeds at the speed of light (ignoring the expansion of the universe)?

It depends on how you are thinking about it or how you frame it, but in the context that I think you mean, the answer is yes (but with the caveat that I'm not sure how useful it is to think of it in that context!).

The surface of last scattering represents the place where the CMBR photons that we currently detect were emitted from. The CMBR photons we currently detect were emitted at a proper distance of around 42 million light-years, around 379,000 years after the Big-Bang. The coordinate they were emitted from was receding from the place where our galaxy finally formed at around 58 times the speed of light at that time.

As time goes on, we expect to detect CMBR photons that were emitted at further distances. At decoupling, the CMBR photons started travelling through space at the speed of light and we might expect to eventually detect CMBR photons that were originally emitted at a distance of 43 million light-years away. Those photons were travelling towards us at the speed of light at that time, but the expansion of the universe (which we cannot ignore) was moving the region of space that they were travelling through away from us at well over 58 times the speed of light at that time.

The surface of last scattering is a conceptual horizon, based on a co-ordinate that is co-moving with the expansion of the universe. Even though we expect to detect CMBR photons that were originally emitted 1 million light-years further away (in terms of proper distance) than the ones we currently detect, it will be a lot longer than 1 million years before we detect them.

If the universe were static (ignoring the expansion, as you said), then that surface of last scattering, the particle horizon, would always recede at the speed of light. It represents the edge of our observable universe, the most distant place from which we have detected photons.

But we cannot consider the surface of last scattering as conceptually receding at the speed of light in the space local to it, if the universe is expanding. Right now, that conceptual horizon is 46 billion light years away and flying past galaxies that currently exist at that distance at multiples of the speed of light.

Consider (as a thought experiment) that we detect a CMBR photon, and then a second later we detect another CMBR photon. Although they are a second apart as we detect them, they were a lot less than 300,000 km apart when they were emitted.


And that an infinite universe or a 3-torus shape (or something like it) is required to maintain homogeneity and isotropy or it would show up as a blue or redshifted CMBR (or there would be a hole in the CMBR)? I guess it would depend on the matter density at the time of emission how visible this would be.

This I am not sure of, hopefully someone else can help here. :)

Sime99
2008-Sep-20, 05:13 PM
Thanks for the detailed reply. It articulates exactly what I was thinking, and I was asking about the static universe model just to confirm my assumptions about the way I was thinking about it. The less GIGO the better.

As to the shape question, I might have phrased it the wrong way round.

Thinking it through:
The universe (in particular the CMBR) looks smooth so we can assume homogeneity and isotropy
Homogeneity and isotropy implies the shape must be one of a,b,c...
If it wasn't smooth or didn't have one of these shapes we should see x,y,z...

The blue/redshifted CMBR was an attempt to think of a consequence of a more lumpy universe than we do see or of a finite unbounded universe where we are not at the centre.

Cougar
2008-Sep-22, 06:23 PM
As to the shape question....

Pick up Janna Levin's quirky little book How the Universe Got Its Spots. Easy, enjoyable reading, and having done research into this very question, she (eventually) speaks directly to this currently confounding question.