How can an infinite universe expand?

Question

I understand the expansion of the universe as actually an increase in the ratio of space to matter. Is this a correct understanding? Otherwise, I don't understand how an infinite structure can expand.

Answer 1

Expansion means that distances are increasing as a function of time. Say if the distance between two galactic clusters is $D$, then in an expanding Universe the distance is governed by some strictly increasing function of time $a(t)$ called the scale factor where

$$D=a(t)D_0$$

where $D_0$ is the distance at the present time and by definition $a(t_{0})=1$.

Cosmology assumes that the Universe is on large scales the same everywhere (homogeneous) and the same in all directions (isotropic) so the above applies to all distances above a certain scale. The scale factor $a(t)$ can be found from the Friedmann equations and initial conditions.

Expansion is possible in Universes of both finite and infinite spatial extent.

As the volume of a (large enough) region of space increases in proportion to $[a(t)]^3$, but the amount of matter remains constant, the matter density changes in proportion to $[a(t)]]^{-3}$. Expansion however also decreases the kinetic energy of of its contents, so the energy density decreases by a greater factor if the contents has kinetic energy.

Answer 2

There is absolutely not contradiction between being infinite and able to expand (in contrast to what your question seems to suggest). This simple fact is not confined to the actual universe we are living in.

As an illustraction, take the infinite 'universe' of the natural numbers $i=0\dots\infty$. Now consider the sets $2i$ and $2i+1$, each equally infinite as the natural numbers, but stretched. Now combine those two sets to get an expanded 'universe' and you obtain the natural numbers again.

Answer 3

How do you describe how far away two points are? You have to have some way of describing the concept of distance.

When we say that the universe is expanding, what we really mean is that distances inside it are increasing.

The idea that the expanding universe is some sort of 3D bubble or balloon that can be seen to expand from outside isn't meaningful, as there is no outside.

Perhaps a more helpful way to think of it is to say that the concept of distance is a property of the universe, and that property is changing over time.

Answer 4

If you he universe is finite in size, something(matter) would have to be present to to fill in the empty space surrounding the entire entire universe or else it would be just more empty space. Let me explain what I mean. A room is finite in size because when you get to a certain point that the walls, floor, and ceiling stop you. So if a universe is finite, it would have to have some equivalent to walls, to keep it the same size and finite and/or to constitute an end. If space ends at some point because nothing can go any further, like if we were inside of an incomprehensibley large hollow sphere and traveled to the end of space and found the end of the universe, something would still be on the other side of whatever the end of the was. Infinite is not a hard concept at all and is really the only possibility if you think a about. Infinite can't expand. It's like a child saying infinite plus one. Only now its college educated grown men now and all the logic in the world wont stop them from trying to make it make sense. The universe is definitely infinite, anyone can observe that by looking up at the night sky. We dont live inside of a cosmic domicile with limited space. We live in infinite empty space on a finite in size spherical shaped mass of a finite amount of matter. an Infinite universe of empty space that has stars and planets, moons and whatever else. But the universe itself is already infinite and therfore can't get any bigger. Its empty space, in every direction, forever(with stars and planets here and there). Why is that so hard for science to accept?

Answer 5

Don't Forget This Part!! The other answers simply explain that an infinite universe can continuously expand because the increase in size is filled with space, not new matter. They confirm your explanation. However, the answer to "how can an infinite universe expand?" requires an explanation of "empty space" and mention of the fact that the universe's expansion is also accelerating.

Empty Space gives physicists headaches. Is there even such a thing as empty space? Or just space filled with matter we cannot yet detect? More on this below.

Accelerating Expansion: The universe is not only expanding, it's speeding up. That keeps some very smart people awake at night. "How can an infinite universe expand?" Well the big bang would explain it... if it were slowing down. It's not. So... it has to be pushed or pulled, right?

Why Does That Happen?

Einstein's theories first predicted that the gravity of the universe would cause the universe to collapse in on itself so he introduced something called the "cosmological constant" in his theory of relativity. That constant enabled the equations to predict a static universe.

Wiki excerpt:

[The cosmological constant] was originally introduced by Albert Einstein in 1917 as an addition to his theory of general relativity to "hold back gravity" and achieve a static universe, which was the accepted view at the time. Einstein abandoned the concept after Hubble's 1929 discovery that all galaxies... are moving away from each other, implying an overall expanding universe.

Modern Understanding

Although Einstein would later call that "cosmological constant" his "greatest blunder", it turned out to be correct. However, he also thought the value would be used to explain why things are static. It turned out the value would explain why things are continually expanding. But what is that constant, besides a number in an equation? Today most physicists seem to think it's dark matter or dark energy. It's a very new science but it is highly researched.

Wiki excerpt from 'Accelerating Universe':

Different theories of dark energy suggest different values of w, with w < -1/3 for cosmic acceleration... The simplest explanation for dark energy is that it is a cosmological constant... this leads to the Lambda-CDM model, which has generally been known as the Standard Model of Cosmology from 2003 through the present...

Wiki excerpt from Dark Energy:

around 70% of the mass–energy density of the universe can be attributed to dark energy. While dark energy is poorly understood at a fundamental level, the main required properties of dark energy are that it functions as a type of anti-gravity, it dilutes much more slowly than matter as the universe expands... The cosmological constant is the simplest possible form of dark energy since it is constant in both space and time

Answering Your Question

So I think the real answer to your question isn't that an infinite universe is possible simply because the amount of empty space increases. Actually, that might not even be possible. There may be no such thing as empty space. Empty space might just be a type of matter we can't see or detect yet.

Wiki:

Dark matter is a hypothetical kind of matter that cannot be seen with telescopes but accounts for most of the matter in the universe. The existence and properties of dark matter are inferred from its gravitational effects on visible matter, on radiation, and on the large-scale structure of the universe. Dark matter has not been detected directly, making it one of the greatest mysteries in modern astrophysics.

To understand the infinite expansion of the universe, ask first how such a thing could be possible. Ask why it expands infinitely instead of the mutual gravity of all the galaxies slowing each other down and causing a collapse.

Answer 6

Think of the universe as a birthday cake. If you had a cake that was a million light years across, you could fit at least a hundred thousand candles on it, right? Probably many more. But just think how many candles you could fit on a cake that was infinite in size - millions, if not billions. But if you put this cake back in the oven and bake a smaller cake onto the side of it, then you could say you've "expanded the cake", despite it being infinite in size. In this way, you could keep adding to your cake until it truly was infinite.

Answer 7

I understand the expansion of the universe as actually an increase in the ratio of space to matter. Is this a correct understanding?

It isn't wrong. The ratio is increasing. But it isn't a "correct understanding". It's merely an observation of one of the results of the expansion of space.

If the universe is infinite how can it expand?

I don't know. Nor do I know how big bang cosmology can be reconciled to an infinite universe. If you look around on the internet, you can find articles like this which say this:

"The linear dimensions of the early universe increases during this period of a tiny fraction of a second by a factor of at least 10$^{26}$ to around 10 centimetres (about the size of a grapefruit)".

However in 2013 results from the WMAP mission appeared to confirm that space is flat. Then a non-sequitur crept in. See this article and pay careful attention to this:

"We now know (as of 2013) that the universe is flat with only a 0.4% margin of error. This suggests that the Universe is infinite in extent; however, since the Universe has a finite age, we can only observe a finite volume of the Universe. All we can truly conclude is that the Universe is much larger than the volume we can directly observe."

That's a massive error. It absolutely doesn't suggest that the universe is infinite in extent. Or that the Universe is much larger than the volume we can directly observe. But this myth has legs, and people repeat it ad-infinitum, even though they can't explain how it fits in with Big Bang cosmology. What you tend to hear is that the observable universe was the size of a grapefruit, but it absolutely doesn't satisfy. Moreover there's a dreadful flaw lurking in the shadows. Take a look at the stress-energy-momentum tensor, and note the energy-pressure diagonal. A gravitational field is something like a spatial pressure gradient, and you can think of space as having an innate "pressure". So you can reason that the universe must expand. As to why Einstein didn't, I just don't know. But anyway, for an analogy, squeeze a stress-ball down in your fist, and let go. It expands because of the pressure. However if that material was infinite in extent, the pressure is counter-balanced at all locations. So it can't expand. In similar vein, in my opinion, an infinite universe can't expand.

People claim the universe must be infinite because of the cosmological principle. But this is merely an assumption. There's an assumption that the universe is homogeneous and isotropic, but this isn't fact. You cannot use it to make sweeping claims about an infinite universe that was always infinite. For all we know some observer 50 billion light years away might be looking up at the night sky wondering why half of it is black. Or a mirror-image of the other. Or some kind of edge.

It is said that in days gone by, people could not conceive of a world that was curved. They could only conceive of a world with an edge. Nowadays I rather fancy that there are some people who cannot conceive of a world that is not curved. They cannot conceive of a world with an edge.

Edit:

See The Foundation of the General Theory of Relativity: "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy". Energy is the source of the stress-energy tensor. Matter is only a source because of the energy-content. Also see Inhomogeneous and interacting vacuum energy which refers to spatial energy. An interesting read is the article Universe 156 billion light-years wide featuring Neil Cornish. This isn't entirely accurate, but the compound interest and the hall of mirrors concepts are of interest. As for the non-sequitur, see this interview with Joseph Silk:

"We do not know whether the Universe is finite or not."

I hope nobody will argue with that. Reading on:

"To give you an example, imagine the geometry of the Universe in two dimensions as a plane. It is flat, and a plane is normally infinite. But you can take a sheet of paper [an 'infinite' sheet of paper] and you can roll it up and make a cylinder, and you can roll the cylinder again and make a torus [like the shape of a doughnut]. The surface of the torus is also spatially flat, but it is finite".

This is akin to the old Asteroids game. But the Planck mission found no evidence of any torus. Reading on further:

"So you have two possibilities for a flat Universe: one infinite, like a plane, and one finite, like a torus, which is also flat."

I dispute that. There is a third possibility. A flat finite universe with no intrinsic curvature. If anybody can cite some reliable sources that support the assertion that a flat universe must be infinite, I'd like to see them.