## more Expanding Universe questions

Study matter and its motion through spacetime...

### more Expanding Universe questions

From my previous thread (which was specifically about light, so I decided to start a new thread if that's okay):

jamest wrote:I watched a BBC documentary this week about the expansion of the universe. It stated (I think) that the expansion of spacetime accounts for the expansion of the universe between galaxies...

jamest @ Expanding space and the wavelength of light

Okay, so now I've been thinking about the snippet above. If what I've stated there is correct then the galaxies/matter aren't moving away from each other; rather, they're being pushed apart by spacetime. So, I have a few questions:

1) Is it safe to assume that this is a roughly spherical event (since I'm assuming the expansion occured from a point, and since I'm also assuming expansion occurs with an equal force in all directions)? I.e., is the universe roughly spherical?

2) ... If so, does this mean that it has a hollow centre [so to speak] since all of the galaxies must now be quite some distance from wherever within the universe the big-bang took place?

3) Does spacetime exist devoid of its relation to matter? I mean, we measure the value of spacetime relative to two+ bodies of matter. It doesn't seem to have any value or [then] 'substance' in isolation of material bodies. I ask this because I'm wondering if spacetime has extended far beyond the galaxies at the outer reaches of the aforementioned sphere? Or do the galaxies themselves (matter) define the actual boundary of the universe? If matter does define the actual boundary of the universe, this would imply [to me] that the expansion of spacetime only occurs within areas where there are matter.

4) I think (please correct me) that there was no matter at the origin of the big bang. If so, and spacetime requires the presence of matter to have any value/substance, then doesn't this create a paradox given '3'?

I might have more questions, but I'll leave it at that for now. Cheers.
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### Re: more Expanding Universe questions

1. The observable universe to the epoch of last scattering aka the Cosmic Microwave Background, is modelled as roughly spherical and gets mapped like this.

and

2. No.
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### Re: more Expanding Universe questions

This may help. It's useful to think of causality when thinking of expanding space. PBS spacetime is a great resource for those of us not formally trained in physics or cosmology. They come out with new episodes approximately weekly.

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### Re: more Expanding Universe questions

I kinda gave up trying to picture these things, I tend to think of it as how the points in space are connected and behave. You could think of expansion as there just being more points, or that the distance between points scales. Of course, adding points to a continuum is kinda weird. How can you tell? Where does the extra 'space' from the added particles come from? I'm not expressing this correctly, don't have the vocabulary.

There was plenty of energy at the big bang, no 'matter', it doesn't matter, matter is energy.

I would like to ask a basic question and this is a decent place without starting a new thread, jamest, if you object, I'll happily remove. So, you don't hear it discussed that often in the lectures I've seen, but to get those great cosmic background images, they have to do a lot pf processing. One thing is they remove all the extraneous signal they pick up from the Milky Way, it's kinda big since we're sitting in it, and I'm not sure how they know what to subtract. My question is about another huge correction that is necessary, removing the artefacts caused by the motion of the earth, really, mostly the galaxy as the sun is carried along with it and the earth along with the sun, this is what it would look like with it uncorrected:

What would it mean to be stationary wrt the background? Is this close to some kind of absolute reference frame? If a bunch of points, spread throughout the observable universe back when the background radiation started, about 3-400K years after the BB, and they were at rest wrt to each other back then, now, they'd be extremely widely spread, and assuming they hadn't been accelerated by anything ever since, for 13 billion years, would they now see the same pattern, in other words, would they still be at rest wrt each other, and see that they had the same velocity wrt the background? Does this have any implications wrt Mach's Principle, that relates to water sloshing out of a bucket if it's rotated?
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### Re: more Expanding Universe questions

crank wrote:
I would like to ask a basic question and this is a decent place without starting a new thread, jamest, if you object, I'll happily remove.

Not at all. This thread is a means to understanding anything to do with universal expansion, which I must confess puzzles me in some regards. Be my guest.
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### Re: more Expanding Universe questions

jamest wrote:
crank wrote:
I would like to ask a basic question and this is a decent place without starting a new thread, jamest, if you object, I'll happily remove.

Not at all. This thread is a means to understanding anything to do with universal expansion, which I must confess puzzles me in some regards. Be my guest.

Thanks, and it's a good subject. Your puzzlement is shared by anyone who knows anything about it, including, of course, the cosmologists.
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### Re: more Expanding Universe questions

The density parameter of the observable universe is equal to one which means it is flat. Were it spherical
it would have to be greater than one. The universe is from a spatial perspective three dimensional so it is
not flat in the Euclidean sense. It appears relatively smooth at the classical level though but not so at the
quantum one. Hence the incompatibility between GR and QM

Space is expanding faster between galaxies as there is no matter to slow it down. It is also expanding within
galaxies but at a slower rate. The Big Bang is still happening so it is wrong to think of it as a past event. It is
also wrong to think of it as a single hypothesis as there are multiple models referencing the beginning of the
observable universe. But they all have a Big Bang within them

The observable universe does not necessarily constitute the entire universe and assuming they re not the same
the boundary cannot be seen. Light cannot be seen beyond the Cosmic Microwave Background. That means the
original point at which the Big Bang occurred cannot be seen either. Although they are only separated by some
380 000 years which in cosmic terms is hardly anything at all
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### Re: more Expanding Universe questions

surreptitious57 wrote:The density parameter of the observable universe is equal to one which means it is flat. Were it spherical
it would have to be greater than one. The universe is from a spatial perspective three dimensional so it is
not flat in the Euclidean sense. It appears relatively smooth at the classical level though but not so at the
quantum one. Hence the incompatibility between GR and QM

Space is expanding faster between galaxies as there is no matter to slow it down. It is also expanding within
galaxies but at a slower rate. The Big Bang is still happening so it is wrong to think of it as a past event. It is
also wrong to think of it as a single hypothesis as there are multiple models referencing the beginning of the
observable universe. But they all have a Big Bang within them

The observable universe does not necessarily constitute the entire universe and assuming they re not the same
the boundary cannot be seen. Light cannot be seen beyond the Cosmic Microwave Background. That means the
original point at which the Big Bang occurred cannot be seen either. Although they are only separated by some
380 000 years which in cosmic terms is hardly anything at all

There are a couple of major errors there. Space expands uniformly everywhere. It's flat in the euclidean sense, triangle's angles add up to 180. At least that's what I've heard a bunch of cosmologists and astronomers, physicists, etc, say in lecture after lecture. Another one is that we're smack in the middle of the point where the big bang occurred, everywhere is in the middle of that point, that point is everything, everything meaning in the observable universe
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### Re: more Expanding Universe questions

jamest wrote:1) Is it safe to assume that this is a roughly spherical event (since I'm assuming the expansion occured from a point, and since I'm also assuming expansion occurs with an equal force in all directions)? I.e., is the universe roughly spherical?

The expansion didn't occur from a single point. It occurred, and continues to occur, everywhere. At scales beyond galaxy clusters, everything is moving away from everything else. So the universe has no centre. As for the shape of the whole universe, nobody knows. Because the age of the universe (or the universe as we know it) is finite - about 13.8 billion years - we can only see a small portion of it, namely the distance that light has been able to travel in all directions, from our point of view, in those 13.8 billion years. We call this the observable universe. The total universe is most likely much larger, but anything that lies beyond the observable universe is inaccessible to us. Therefore, the best thing we can do is assume that the rest of the universe doesn't look radically different from what we can observe, and extrapolate. It's like trying to figure out the shape of the Earth from what we can see from our backyard.

So what could the shape of the whole universe be like? Well, if we assume that the universe looks roughly the same everywhere, and that it has no centre, there are only a few possibilities. The simplest are:

a) The universe is infinite (but expanding!), and looks like good old Euclidean space at all times, with no overall curvature.

b) The universe has the same positive curvature everywhere, which leads to the shape of a three-dimensional sphere. Compare this to the surface of a planet or a star, which is (approximately) a two-dimensional sphere. Indeed, the surface of the Earth has no centre and looks roughly the same everywhere. The universe would be a three-dimensional equivalent of this, which is pretty mind-bending.

c) The universe has the same negative curvature everywhere. That's even harder to imagine, because there is no 2D equivalent of this. Textbooks will often draw something that looks like a saddle surface, but that's only an approximation.

Our observations indicate that the curvature of the universe is very close to zero, so option a is our best bet (but b and c can't be ruled out). An obvious question would be how an infinite universe can be reconciled with a big bang. If the age of the universe is finite, shouldn't the size of the universe be finite as well? That's indeed a tricky issue. However, it's important to emphasize that the notion of a big bang singularity is itself a speculation. We don't really know what happened in the very early stages of the universe, let alone how it all began (if it had a beginning at all). All we can say is that the universe is evolving from a state with high density to a state with low density. When we say that the universe is 13.8 billion years old, what we really mean is that our knowledge of physics and our data allow us to go back 13.8 billion years in time. Beyond that, we don't have any real answers.
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### Re: more Expanding Universe questions

I keep hearing that the universe is flat, but I would have thought that the increasing rate of expansion implies negative curvature.
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### Re: more Expanding Universe questions

Manticore wrote:I keep hearing that the universe is flat, but I would have thought that the increasing rate of expansion implies negative curvature.

No, the curvature is determined by the total density of the universe, and whether it is larger than, equal to, or lower than a particular value at any given time, called the critical density: if the total density is equal to the critical density, then the curvature is zero. If the total density is larger than the critical density, the curvature is positive. If the total density is smaller than the critical density, the curvature is negative. Also, the sign of the curvature cannot change, so if it is zero today, then it has always been zero and it will always remain zero; likewise for positive and negative curvature.

The total density consists of radiation, matter, and dark energy. So in itself, dark energy doesn't determine the sign of the curvature. However, dark energy does have an interesting property: it makes the universe 'flatter'. That is, it pushes the curvature asymptotically closer to zero (if it isn't zero already). Inflation theory relies on the same property, which is one of the reasons why inflation is being proposed to explain why the present-day curvature of our universe is so close to zero.
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### Re: more Expanding Universe questions

An interesting, flat, universe shape example is the cylindrical case. This can be represented by a cube, where opposite faces are connected. You've all seen something like this, it's how a lot of video games, at least old ones, wrap the screen from top to bottom and left to right. If something goes off the 'edge' of the cube, it enters the other. There's no curvature, it's flat, it's just the ways the points are connected. These can start getting weird if you invert the connection, and other stranger arrangements This example is a flat, finite, unbounded universe. And, no, there is nothing 'outside' this universe.

A great book to read on this is The Shape of Space
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### Re: more Expanding Universe questions

Understanding how a straight line can be curved, the geodesic explanation:

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### Re: more Expanding Universe questions

Pulsar wrote:
Manticore wrote:I keep hearing that the universe is flat, but I would have thought that the increasing rate of expansion implies negative curvature.

No, the curvature is determined by the total density of the universe, and whether it is larger than, equal to, or lower than a particular value at any given time, called the critical density: if the total density is equal to the critical density, then the curvature is zero. If the total density is larger than the critical density, the curvature is positive. If the total density is smaller than the critical density, the curvature is negative. Also, the sign of the curvature cannot change, so if it is zero today, then it has always been zero and it will always remain zero; likewise for positive and negative curvature.

The total density consists of radiation, matter, and dark energy. So in itself, dark energy doesn't determine the sign of the curvature. However, dark energy does have an interesting property: it makes the universe 'flatter'. That is, it pushes the curvature asymptotically closer to zero (if it isn't zero already). Inflation theory relies on the same property, which is one of the reasons why inflation is being proposed to explain why the present-day curvature of our universe is so close to zero.

As I remember it, we decided the universe was flat due to the apparently constant expansion rate. We then tweaked the amount of dark matter slightly to make the density come out right.
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### Re: more Expanding Universe questions

I thought the best evidence of flatness was the geometry observable in the cosmic background radiation. There are spatial patterns with particular wavelengths which lead to particular angular sizes and this shows the universe is flat.
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### Re: more Expanding Universe questions

crank wrote:I thought the best evidence of flatness was the geometry observable in the cosmic background radiation. There are spatial patterns with particular wavelengths which lead to particular angular sizes and this shows the universe is flat.

I was thinking of when I was involved in astrophysics - a period which ended before the COBE satellite was launched.
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