Homogeneity and isotropy in Big Bang model

[Goddar]

Hi there.
I'm having a hard time understanding the precise meaning of the so called "cosmological principle":
My understanding of the general Big-Bang model is that far enough back in time the observable universe came down to something very small (compared to now), very dense, very hot... Ok, i would have other questions about that but it's not the topic here.
So, the next picture is one of this "small" universe spreading incredibly, part of which probably due to inflation (but maybe not?), the other part comparable to the way a gas concentrated in a small region would rapidly spread due to random motion of its particles.
Now in this picture i don't see how to justify the assumption of homogeneity throughout all space: it seems that there is a natural, effective center of momentum in the universe and we can expect homogeneity at a given radius from this center (in terms of matter density and therefore metric as well), and also isotropy with respect to this center, but certainly not for any arbitrary point in the observable universe... Also, say we're standing at the edge of this universe: there's certainly no sense of homogeneity and isotropy so what is wrong with my understanding, please?
This might be very basic but i doubt I'm the only beginner in Cosmology who doesn't understand it...
Thanks!

 

[Chalnoth]

It seems that you are visualizing the universe as a lump of gas that started expanding. This is false. There is no reason to believe that there is any edge to the universe, and certainly if there is anything like an edge it's far beyond our horizon such that it has no impact. Either way, it is valid to conceptually think of the universe as being infinite in every direction. Early-on, it wasn't small, it's just that things were closer together.

 

[phinds]

And to add to what Chalnoth said, you seem to be envisioning a center, but there was no center. The initial event happened throughout the entire universe, whatever size it was (infinite or otherwise) not at some single point. I realize you probably already know this, but just to be clear, "singularity" does not mean "point" it just means "the place where, if you extrapolate backwards in time, the math model breaks down and we don't know what was really going on".

 

[Goddar]

Thanks for the reply.

It seems that you are visualizing the universe as a lump of gas that started expanding. This is false.

Ok. Then what's the right picture (in Big Bang model, i mean)?

There is no reason to believe that there is any edge to the universe, and certainly if there is anything like an edge it's far beyond our horizon such that it has no impact.

I meant an "edge" in the sense that a Big Bang model seems to suppose a finite amount of matter (maybe locally? there could be many local Big Bangs..), and this matter would be spread within a finite volume of space (regardless of how space would even be defined outside of it), which volume would then necessarily have an "edge"?..

Either way, it is valid to conceptually think of the universe as being infinite in every direction. Early-on, it wasn't small, it's just that things were closer together.

Well the universe may or may not be infinite and we'll probably never have the answer to that, but that's not really the question here, i think... I understand the universe was "closer together", that's what i really meant by saying "compared to now", but that doesn't seem to undermine the picture of an expanding ball...

 

[Goddar]

Thanks, Phinds.
I understand your point; it seems though that we can still determine an effective "center" (i.e. the center-of-momentum) at any time? That would seem to make the isotropy principle only valid with respect to this point (and i don't mean in some absolute space, but in a purely relational sense..)?

 

[phinds]

Thanks, Phinds.
I understand your point; it seems though that we can still determine an effective "center" (i.e. the center-of-momentum) at any time? That would seem to make the isotropy principle only valid with respect to this point (and i don't mean in some absolute space, but in a purely relational sense..)?

No, there is no center of momentum. Everything is moving away from everything else. No edge, no center. Hard to get your head around at first, I know. It seems sort of "human nature" to believe there has to be a center and an edge, but it just doesn't work that way.

Even if the universe is not infinite, it is almost certainly unbounded, so still no edge and no center.

The universe didn't expand into anything, it just expanded. Weird, but true to the best of our understanding.

 

[Goddar]

Yep, indeed it's starting to sound like black magic...
I'm not going to insist because i hate to be annoying but indulge me one last bit, please.

So to be clear we're talking about a universe that doesn't necessarily require extra-dimensions and where the metric is nearly flat;
Let's imagine this universe, whatever process has made it happen, has produced only a handful of galaxies (say, 3), which are moving away from each other at non-relativistic but slowly accelerating speeds;
Passengers on these galaxies (i.e. at rest with respect to their respectful galaxies), once they figured their relative velocities and accelerations, can always agree on a unique center of momentum, which is the center of mass at any time and is independent of the coordinates' system. Right?
Then the "edge" of this universe is, entirely subjectively but straight-forwardly, understood as the triangle formed by these three objects at any time.

Now just add a few billion galaxies and the same concepts can still be applied, so what goes wrong here and what's the alternative picture i can't seem to grasp?

 

[Orodruin]

You seem to imagine that expansion means that galaxies are moving away from each other. This is not the idea but a very common misconception. It is not galaxies which are moving but space itself that is expanding. There is a cosmologically preferred frame (the CMB frame), but that is only ever going to give you a preferred velocity, not a point in space. Regardless of where you are, if you are a comoving observer (ie, at rest relative to the CMB) the Universe will look the same wherever you are.

 

[timmdeeg]

@: Goddar, have you seen this?

http://www.phinds.com/balloonanalogy/

 

[phinds]

@: Goddar, have you seen this?

http://www.phinds.com/balloonanalogy/

Yeah, I should have pointed that out myself. I forget about it sometimes. On the other hand, I don't really say anything much in it that I haven't said in this thread, just more of it.

 

[Goddar]

Thank you, Orodruin. (and others, sorry i hadn't seen yet!)

You seem to imagine that expansion means that galaxies are moving away from each other.

Yes, i always understood that this is what was observed (i mean on average: i know they can also cross paths, collide or even orbit each other at times..);

It is not galaxies which are moving but space itself that is expanding.

My understanding (so far) was also that the interpretation of space itself expanding is suggested by the accelerating rate but "moving away" is still what we observe?
Now if we observe that the universe looks exactly the same in every direction and there is no sense of a historical Big-Bang "zone" (with respect to every observable thing) and space itself expands then it sounds like the universe lives on a 3-sphere (the surface of a 4-ball), hence the usual analogy of a 2-sphere...
Now this is a closed surface so it would also mean that by going any direction for a long time, a traveler or light ray would come back to its sender?.. Would also suggest embedding in a 4th dimension...

 

[timmdeeg]

Yeah, I should have pointed that out myself. I forget about it sometimes.

Don't worry, you can always rely on me.

My understanding (so far) was also that the interpretation of space itself expanding is suggested by the accelerating rate but "moving away" is still what we observe?
Now if we observe that the universe looks exactly the same in every direction and there is no sense of a historical Big-Bang "zone" (with respect to every observable thing) and space itself expands then it sounds like the universe lives on a 3-sphere (the surface of a 4-ball), hence the usual analogy of a 2-sphere...
Now this is a closed surface so it would also mean that by going any direction for a long time, a traveler or light ray would come back to its sender?.. Would also suggest embedding in a 4th dimension...

Regardless his position in the universe, an arbitrary observer will see the galaxies moving away. In terms of "true physics" one can only say that the distances between commoving objects are increasing. The notion of expanding space itself like a substance analogously to the rubber in said analogy is just a picture, not wrong, but not true physics.
You are right, the balloon analogy stands for a spherical universe, which would be finite. According to the data it is spatially flat however. Regarding this aspect it's better to think of an expanding rubber sheet (which is infinite) therefore.

 

[Bandersnatch]

Now this is a closed surface so it would also mean that by going any direction for a long time, a traveler or light ray would come back to its sender?.. Would also suggest embedding in a 4th dimension...

With accelerated expansion the light signal sent from sufficiently far away will never reach an observer, so even in a closed universe you don't get to see the back of your head - you are confined to a limited region of observable universe.
Space being closed also doesn't necessarily imply embedding in higher-dimensional space. One can have a perfectly defined curved, closed space without the need for any higher dimensions. For example, in the balloon analogy, the third dimension is unnecessary to describe how the geometry of the surface behaves. It's easier to visualise by placing it in 3D, but not necessary.

 

[Goddar]

Thanks for the input, guys.

You are right, the balloon analogy stands for a spherical universe, which would be finite. According to the data it is spatially flat however. Regarding this aspect it's better to think of an expanding rubber sheet (which is infinite) therefore.

Ok. The other, more obvious interpretation would be that we happen to sit on a more or less central region of an expanding-ball like universe but i understand this is discarded on the grounds that we have no reason to feel special... still possible though, since homogeneity and isotropy are still assumptions?..

With accelerated expansion the light signal sent from sufficiently far away will never reach an observer, so even in a closed universe you don't get to see the back of your head - you are confined to a limited region of observable universe.

Not really getting that: in the 2D analog the signal does eventually hit the back of your head unless the universe foils on itself like an "infinite" onion or expansion has reached light-speed radially. In 3D the same logic should follow, it seems..

Space being closed also doesn't necessarily imply embedding in higher-dimensional space. One can have a perfectly defined curved, closed space without the need for any higher dimensions. For example, in the balloon analogy, the third dimension is unnecessary to describe how the geometry of the surface behaves. It's easier to visualise by placing it in 3D, but not necessary.

Point taken. Thought about it after posting, actually.. Still a sensible temptation, maybe?

 

[phinds]

One thing you might not be aware of is this: "the universe" is generally taken to either infinite or to be many orders of magnitude greater than the observable universe and things at the edge of the observable universe are now receding from us at about 3c and everything farther away than that is receding even faster, so the "wrap-around" topology still absolutely does not mean that you could ever see the back of your head.

 

[Goddar]

Right, i get that. With large enough "universe", expansion will work to make a signal never reach back..
Probably time to wrap-up this post and dig more into the literature.
Thanks, guys!