# In a finite universe, what happens when light reaches the boundary?

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If a universe is finite and is not expanding at a speed equal to or greater than c, what happens when light or another form of electromagnetic radiation traveling reaches the boundary?

This is one of the most essential questions in cosmology. The first gedankenexperiment probably. If the universe were finite what could be at the boundary? If there were some sort of wall, what would be on the other side? Can space just end? What would stop one from pushing past the end? If you extend your arm out past the end does your arm cease to exist? It is because we cannot provide any logically consistent answers to these questions that we accept that there are only two possibilities for the boundaries of the universe: 1) the universe is infinite and has no boundaries or 2) the universe is finite, but bends around and closes in on itself like the surface of a sphere and has no boundaries. That is, there are no boundaries. Alternative 2 then forces one to contemplate that there is at least one more dimension to space then the known 3.

One important concept that has not been mentioned yet is the "cosmological principle." This is the key simplifying idea for our cosmological models, it says that the universe is the same everywhere on the largest scales at a given age, so alien astronomers 50 billion light years from us that also conclude the universe is 13.8 billion years old will be observing pretty much all the same things we are. This principle is not proven by data, but the data is consistent with it, most notably the Hubble law and the homogeneity of the cosmic microwave background. It allows us to understand the past of our own part of the universe by seeing the past of distant parts (a constraint we are stuck with given the speed of light).

So that's why a universe model that is finite in size must curve back on itself-- nothing else would satisfy the cosmological principle. This doesn't mean the principle is true, it means we are not going to part with it unless we have to.

## Is there a boundary present for our universe?

Correct me if I'm wrong, but couldn't you have an unbounded universe that has a boundary, similar to a balloon (has boundary, but if you go straight, you'll just end back up at the starting point)?

I'm not sure of the various models, but I thought I've seen that mentioned somewhere on PF.

Correct me if I'm wrong, but couldn't you have an unbounded universe that has a boundary, similar to a balloon (has boundary, but if you go straight, you'll just end back up at the starting point)?

I'm not sure of the various models, but I thought I've seen that mentioned somewhere on PF.

D'oh! You're absolutely correct. I completely spaced on that.

As a follow up, would it be possible the curvature of space time at the boundary appear that it is boundless like the surface of a balloon, or would that still be considered a bounded system?

Apologies, I can't quite follow your question. I think there's still some confusion, and not unexpectedly so, considering the nomenclature.

Bounded means basically the same as "finite". Unbounded is then infinite. As in, we don't know whether the universe is bounded or not = we don't know if it's finite or infinite.
Boundary means the same as "edge". E.g., the observable universe is bounded has a boundary = it's got an edge (beyond which we can't see), but the Universe as a whole doesn't.

Perhaps we should stick to "in/finite" and "edge" as they are less prone to getting confused with each other.

Could you try and reword your question using those terms?

(mind you, this is all talking about space, not space-time)

Apologies, I can't quite follow your question. I think there's still some confusion, and not unexpectedly so, considering the nomenclature.

Bounded means basically the same as "finite". Unbounded is then infinite. As in, we don't know whether the universe is bounded or not = we don't know if it's finite or infinite.
Boundary means the same as "edge". E.g., the observable universe is bounded = it's got an edge (beyond which we can't see), but the Universe as a whole doesn't.

Perhaps we should stick to "in/finite" and "edge" as they are less prone to getting confused with each other.

## What happens to EM waves outside the universe?

There is no outside the Universe nor is there an edge. Its also not known if the universe is finite or infinite.

Or read this FAQ for further details.

several I've already posted the FAQ sub forum and Ned wrights FAQ.

here is a useful balloon analogy

this site describes loosely a few finite shapes with no edge.

this on going thread also has tons of descriptions and information on edge and shape

also keep in mind the shape of what is called the Observable universe is finite and spherical. The observable universe is simply defined as the furthest we can measure. Due to speed of light and expansion.

astrophysics is complicated for the casual reader (like me) because there are usually several different theories illustrating a single concept, example the shape of the local universe or the shape of the entire universe. to make communication easier many of the theories are reduced to initials or a tag name. this complicates thing a lot for the casual reader.

Keep reading. It took me a week and a half to get thru this article the first time I read it. I had 40 pages of notes that I looked up to get through this one page

astrophysics is complicated for the casual reader (like me) because there are usually several different theories illustrating a single concept, example the shape of the local universe or the shape of the entire universe. to make communication easier many of the theories are reduced to initials or a tag name. this complicates thing a lot for the casual reader.

Keep reading. It took me a week and a half to get thru this article the first time I read it. I had 40 pages of notes that I looked up to get through this one page

yes of course. I should have given more thought in selecting my example.

Edit - maybe my point was to read astrophysics you have to have a vast underpinning of knowledge. how I got here is I was reading quantum physics. read how the quantum vacuum was related to the cosmological constant. Thus came in to search around the forum. Interesting place

A major outstanding problem is that most quantum field theories predict a huge value for the quantum vacuum. A common assumption is that the quantum vacuum is equivalent to the cosmological constant. Although no theory exists that supports this assumption, arguments can be made in its favor.

Such arguments are usually based on dimensional analysis and effective field theory. If the universe is described by an effective local quantum field theory down to the Planck scale, then we would expect a cosmological constant of the order of M_< m pl>^4. As noted above, the measured cosmological constant is smaller than this by a factor of 10−120. This discrepancy has been called "the worst theoretical prediction in the history of physics!".

Some supersymmetric theories require a cosmological constant that is exactly zero, which further complicates things. This is the cosmological constant problem, the worst problem of fine-tuning in physics: there is no known natural way to derive the tiny cosmological constant used in cosmology from particle physics. Structural Quantum Gravity is an approach of Quantum Gravity that predicts Einsteins field equations with cosmological constant as the classical limit of the action of Structural Quantum Gravity.

It's impossible to know whether the universe if finite or infinite because we'll never be able to see it all. Note that genneth says "and for simplicity the universe is infinite", and this is the key point really. It makes Physics simpler if the universe is infinite so we tend to assume it is.

But you need to consider what you mean by "infinite". It doesn't make sense to say the universe has an edge, because you then have to ask what happens if you go up to the edge then take one more step. That means the only alternative to the universe being infinite is that it loops back on itself like a sphere, so you can walk forever without reaching an edge, but eventually you'll be back where you started.

We don't think the universe is like a sphere because for that spacetime would have to have positive curvature, and experiments to date show space is flat (to within experimental error). However spacetime could be positively curved but with such small curvature that we can't detect it. Alternatively spacetime could be flat but have a complex global topology like a torus. The scale of anything like this would have to be larger than the observable univrse otherwise we'd have seen signs of it.

Incidentally, if the universe is infinite now it has always been infinite, even at the Big Bang. This is why you'll often hear it said that the Big Bang wasn't a point, it was something that happened everywhere.

I've just realised that you also asked the question about time beginning at the Big Bang. In the answer to that question I explained how you use the metric to calculate a geodesic, with the result that you can't calculate back in time earlier than the Big Bang. You can also use the metric to calculate a line in space at a fixed value of time (a space-like geodesic). Our universe appears to be well described by the FLRW metric with $Omega$ = 1 that I mentioned in the other question, and if you use this metric to calculate your line you find it goes on forever i.e. the universe is infinite.

But then no-one knows for sure if the FLRW metric with $Omega$ = 1 is the right one to describe our universe. It's certainly the simplest.

If you model the universe as the surface of a sphere, then this is a finite universe but which has no boundary. Thus, it makes perfect sense to have a finite universe but which has no "edge."

Read How the Universe Got Its Spots by Janna Levin and then go read Ned Wright's Cosmology Tutorial website again. I swear to you that you will have a tough time believing the universe can be endless. It’s funny how that happens. Janna’s book is thin and easy. There’s no college math, no raisin bread and no balloons. Instead, it’s all the different possibilities and how to interpret the CMB and that kind of thing.

An endless universe has its issues. It needs an infinite mass at the time of the Big Bang. That means infinite galaxies and infinite worlds. So there must be one just like ours, in fact infinite worlds just like ours. Even so, I prefer an infinite universe too. But it’s nothing more than a preference.

The problem with the "balloon" analogy is that, while it may make sense in 2 dimensions, we live in 3 dimensions. and there is no 3-D analogy, which is why it makes no sense.

A finite universe with no boundary/edge is difficult (if not impossible) to imagine or envision. which also makes it hard to believe.

This is one of those subjects that the cosmology community continually states as a "fact" when there is no way to verify it as such. nor will there ever be.

From what I am hearing the accepted theory by most modern theoretical physicists and cosmologists today is the fact that our universe is one of many in a so called "Cosmic Landscape". In other words, we can tell the that our present universe is constantly expanding everywhere all the time because of the cosmological constant and creation of dark energy.

However, the theory that is most strong today is that our universe (and all of it's physical laws) originated from another bigger expanding universe that we cannot see yet because of its enormity. This universe in turn, grew out of an even bigger universe that was expanding rapidly say 30 billion light years ago. etc. etc. So as we know it, there are several "megaverses" that were here and expanding before our universe is, and that will continue to develop more universes each with their own "Big Bang" that will grow and expand from our universe as we know it.

This is known as the "pocket universe" theory or a "universe born within another universe" type of theory.

Note: Each of those universes that preceded ours or will that should be created from within ours will have different physical laws and properties than our universe does (ie- different cosmological constants, different strengths for each of the four fundamental forces, perhaps more or less than four fundamental forces. etc.)

Basically every universe created from other universes will have variety. String theory accounts for all of this happening I heard.

Have to be more clear. There was a temporary union of two ideas----the string landscape (now out of fashion among string theorists) and the multiverse resulting from the eternal inflation scenario.

Your word "most" is probably inaccurate. String theorists are a minority of theoretical physicists. The landscape bunch was a minority within a minority.
This year's annual meeting (Strings 2008) has no landscape talks scheduled.
The landscape fad was mainly 2003-2007. At what was probably the height, in 2005, they had an informal poll at the annual meeting (Strings 2005) and rankandfile string theorists voted AGAINST landscape thinking by about 3 to 1. Steve Shenker, who was leading the panel+audience discussion and who posed the question was heard to say "holy shît" when he saw the hands raised in the auditorium. It surprised a number of prominent string leaders, who at that time were promoting landscape ideas.

Again, amongst cosmologists, only a small minority study inflation scenarios. It would be an exaggeration to say that the multiverse of eternal inflation is "accepted" by any but a small minority. The business of bubble universes or pocket universes is mainly speculation by a few. For ordinary working cosmologists, one universe with one inflation episode at the beginning is enough for them to investigate and be concerned with.

So when you look at the cosmology research papers being published in the professional journals you don't see very much about multiverse or eternal inflation---you see research into models of our universe.

We shouldn't confuse landscape ideas with the fact that the standard model universe extendes beyond what is directly observable. The latter is normal. It is just part of the consensus picture of the universe that cosmologists work with. The observable portion is a small part of the whole thing. The whole can be finite spatial volume, or infinite----they are still working on determining which.

No reason to assume that physical laws and conditions are any different in the part we cant see from how they are here in the part we can see. No reason to speculate about a landscape just because the observable portion is not the whole thing.

Basically there was a buzz about cosmic landscape and it looks now as if it might be quieting down. One sign being that it seems to be less fashionable now with string theorists---as I said the schedule for the main annual conference Strings 2008 at the present has no landscape talks scheduled. If string people stop promoting it, probably the whole thing will get a flat tire. (just my guess)

## Where is the edge of the universe?

As far as we can tell, there is no edge to the universe. Space spreads out infinitely in all directions. Furthermore, galaxies fill all of the space through-out the entire infinite universe. This conclusion is reached by logically combining two observations.

First, the part of the universe that we can see is uniform and flat on the cosmic scale. The uniformity of the universe means that galaxy groups are spread out more or less evenly on the cosmic scale. The flatness of the universe means that the geometry of spacetime is not curved or warped on the cosmic scale. This means that the universe does not wrap around and connect to itself like the surface of a sphere, which would lead to a finite universe. The flatness of the universe is actually a result of the uniformity of the universe, since concentrated collections of mass cause spacetime to be curved. Moons, planets, stars, and galaxies are examples of concentrated collections of mass, and therefore they do indeed warp spacetime in the area around them. However, these objects are so small compared to the cosmic scale, that the spacetime warping which they cause are negligible on the cosmic scale. If you average over all of the moons, planets, stars, and galaxies in the universe in order to get a large-scale expression for the mass distribution of the universe, you find it to be constant.

The second observation is that our corner of the universe is not special or different. Since the part of the universe that we can see is flat and uniform, and since our corner of the universe is not special, all parts of the universe must be flat and uniform. The only way for the universe to be flat and uniform literally everywhere is for the universe to be infinite and have no edge. This conclusion is hard for our puny human minds to comprehend, but it is the most logical conclusion given the scientific observations. If you flew a spaceship in a straight line through space forever, you would never reach a wall, a boundary, an edge, or even a region of the universe without galaxy groups.

But how can the universe have no edge if it was created in the Big Bang? If the universe started as finite in size, shouldn't it still be finite? The answer is that the universe did not start out as finite in size. The Big Bang was not like a bomb on a table exploding and expanding to fill a room with debris. The Big Bang did not happen at one point in the universe. It happened everywhere in the universe at once. For this reason, the remnant of the Big Bang, the cosmic microwave background radiation, exists everywhere in space. Even today, we can look at any corner of the universe and see the cosmic microwave background radiation. The explosive expansion of the universe was not the case of a physical object expanding into space. Rather, it was a case of space itself expanding. The universe started out as an infinitely large object and has grown into an even larger infinitely large object. While it is difficult for humans to understand infinity, it is a perfectly valid mathematical and scientific concept. Indeed, it is a perfectly reasonable concept in science for an entity with infinite size to increase in size.

Note that humans can only see part of the entire universe. We call this part the "observable universe." Since light travels at a finite speed, it takes a certain amount of time for light to travel a specific distance. Many points in the universe are simply so far away that light from these points has not had enough time yet since the beginning of the universe to reach earth. And since light travels at the very fastest speed possible, this means that no type of information or signal has had time to reach the earth from these far away points. Such locations are currently fundamentally outside our sphere of observation, i.e. outside of our observable universe. Every location in the universe has its own sphere of observation beyond which it cannot see. Since our observable universe is not infinite, it has an edge. This is not to say that there is a wall of energy or a giant chasm at the edge of our observable universe. The edge simply marks the dividing line between locations that earthlings can currently see and locations that we currently cannot. And although our observable universe has an edge, the universe as a whole is infinite and has no edge.

As time marches on, more and more points in space have had time for their light to reach us. Therefore, our observable universe is constantly increasing in size. You may think therefore that after an eternity of time, the entire universe will be observable to humans. There is, however, a complication that prevents this. The universe itself is still expanding. Although the current expansion of the universe is not as rapid as during the Big Bang, it is just as real and important. As a result of the expansion of the universe, all galaxy groups are getting continually farther away from each other. Many galaxies are so far away from the earth that the expansion of the universe causes them to recede from the earth at a speed faster than light. While special relativity prevents two local objects from ever traveling faster than the speed of light relative to each other, it does not prevent two distant objects from traveling away from each other faster than the speed of light as a result of the expansion of the universe. Since these distant galaxies are receding away from earth at a speed faster than light, the light from these galaxies will never reach us, no matter how long we wait. Therefore, these galaxies will always be outside of our observable universe. Another way of saying this is that although the size of the observable universe is increasing, the size of the actual universe is also increasing. The edge of the observable universe cannot keep up with the expansion of the universe so that many galaxies are eternally beyond our observation. Despite this limitation on observational abilities, the universe itself still has no edge.

## If the universe had a definite boundary, what would it look like, what would we see?

Just a gentle reminder that r/AskScience aims to provide in-depth answers that are accurate, up to date, and on topic. You should only answer questions if you have expertise in a topic and can provide sources for your answer if asked. For more details please refer to our guidelines.

It's very unlikely that the universe would have an actual boundary. We don't expect to come across an unbreakable wall in space, that would be weird.

There are two possibilities :

The universe is finite, but has no boundary. The universe would be looping on itself, and when you travel to one edge you just end up on the other side. This is the 3D equivalent of a pac-man world, in which when you cross the boundary on one side you're back on the other.

The universe being infinite is mind boggling enough, but I can't even begin to grasp the concept of a the pac-man universe. I understand pac-man, obviously, but it just seems so weird and foreign.

Like, If I stood at the edge of the universe on the far left side, and you stood at the edge on the far right, weɽ simultaneously be very far away from each other and also very close. i think. or would we just be close since our position is relative?

As others point out, the universe probably doesn't have a definite boundary, and even if it did it is outside the observable universe. However, that shouldn't prevent us from imagining what such a boundary could look like.

From a General Relativity perspective, there are several ways of designing a universe with a a definite boundary. The simplest one is probably the reflecting boundary condition. Here is a toy metric with that property:

ds 2 = -Heaviside(x) -1 dt 2 + dx 2 + dy 2 + dz 2

This metric has an infinitely tall gravitational potential for x<0 (Heaviside(x) is the Heaviside step function, which is 0 for x<0 and 1 for x>0. I'm using it here because I assume you want a hard edge rather than a fuzzy edge), making it impossible for anything to move past it. All matter and radiation would be reflected, so it would look like a perfect mirror. Flying into it with your spaceship would be like flying into a copy of yourself coming from the opposite direction.

(It might be tempting to use the metrix ds 2 = -dt 2 + Heaviside(x) dx 2 + dy 2 + dz 2 , since that looks like a metric where the x coordinate becomes meaningless for x<0. But this doesn't actually work - it's just an extreme unit change for x<0).

More complicated behavior is also possible. For example, space could become 1-dimensional:

ds 2 = -dt 2 + dx 2 + Heaviside(x)(dy 2 +dz 2 )

or fray into a web of rolled-up dimensions, or whatever.

However, all of this falls into the domain of "metric engineering". I'm just writing down these metrics without any accompanying explanation for how they would arise, or whether they would be stable, etc.. I'm not aware of any reasonable theory that predicts a hard edge to the universe like this.

If the observable universe is X years old but its really infinite, does that mean it's actually infinite light years old/long? I'm not even sure if I'm asking this right

Man, this was tough to read as someone with no understanding on the subject.

Seeing such higher level of thinking really makes me jealous. I want to know as much as I can! (College needs to be cheaper..)

What would be on the other side of that hard edge, and how would that hard edge affect space expanding metrically?

If the universe was a closed system with a perfect mirror edge then would everything in it eventually heat up as all the radiated energy given off by well everything gets reflected back and re-absorbed by something else.

Hmm, so what would happen if you flew a space ship into one of those hypothetical "border regions" where our physics break down? Does everything just fall apart and die or would all of our matter and energy convert itself to the new normal?

If the observable universe is X years old but its really infinite, does that mean it's actually infinite light years old/long? I'm not even sure if I'm asking this right

Could some of the phenomenon we've observed that defy our current knowledge of physics be in other bubbles that we can observe for some reason then?

Doesn't the Borde-Guth-Vilenkin theorem (link) apply to inflation too?

"Thus inflationary models require physics other than inflation to describe the past boundary of the inflating region of spacetime."

To start, making a reply to this question within the rules of "AskScience" is practically improbable. The question is setting an environmental variable that is in its own nature "speculative". The answer would fall into the category of speculation because we have to define what the boundary is. We can only speculate on what the boundary is, because we don't know for a fact what the boundary is. As such, this question should be a discussion.

In order for the human eye to see something, there must be energy particles radiating from this boundary that are inside the human eye's visibility range. Otherwise, there must be energy particles radiating that an instrument can detect and report said anomaly.

If the boundary is an endless void, it really is not a boundary, and matter or energy can move beyond it and back. This is basically an observed boundary because nothing exists beyond this point. Anything that leaves beyond this point has no means to return, as there is nothing to act upon to have an equal and opposite reaction.

If the boundary acts like the context of a blackhole where anything that passes beyond will never return, then there is nothing to radiate light and nothing to bounce radiated light from. Therefore, it will appear as an endless void, and anything that passes into it will disappear, forever. This is a special applied case of the endless void, except the boundary actually exists in nature.

If the boundary does not allow anything to pass beyond it, never lost to an endless void or blackhole condition, then anything hitting that boundary should bounce off of it, perfectly. As such, it should appear like a perfect mirror. If this boundary does not perfectly reflect everything, then that means matter or energy can be destroyed. Otherwise, it is a wall that could be broken through, and therefore no longer qualifies as a boundary to the universe.

Alternatively if the boundary does not reflect everything that hits it perfectly, there is a special unknown anomaly that can create a visible wall on some spectrum where whatever hits it is converted from one arrangement of matter or energy into another energy, and yet all energy and matter hitting this barrier must be released elsewhere along the barrier. Under this condition, I have no idea what such a boundary would look like unless I know how the energy and matter return from it.

For the last consideration of a possible boundary, I must set this example with navigating the surface of Earth. If I move in one direction, I will never reach an "end" to the Earth because the surface wraps around a sphere, but the surface of this sphere has a finite area. Due to that finite area, we can draw the surface like a map, setting "boundaries" where moving beyond one boundary wraps you around to the other side of the map, or basically the map repeats itself beyond that "boundary". Consider this boundary in the universe, you would continue to see the universe, as the universe would continue infinitely but has a finite volume of space that can be mapped and such imaginary boundaries set for where the map repeats itself.

Another note, nothing can radiate from beyond this boundary because nothing else exists beyond the boundary, except for the case where space has finite volume but repeats itself in every direction.

## Does the UNIVERSE have a boundary or OUTER LIMIT?

What would you expect to see if you were to reach this boundary?

I believe the only limit to the universe is in our imagination, I feel it's beyond our minds to try and put a limit or draw a boundry.

Might be a good place to see if you have any control issues.

I hadn't ever really thought about it but off the top of my head I'd guess I agree with husker's comment.

If I was able to travel to a "boundry" at the edge of teh universe what would happen if i crossed that boundry? I'd either cease to exist of just continue on. If I just continued on then am I really in another universe or was the boundry false? If I ceased to exist than I guess the whole point would be moot for me eh?

This one of the questions that sometimes comes up when I'm out with these two friends of mine, Brian and Ted, and we then realize that our heads are too small and our brains too slow, to sample the question " Is there a boundary out there?"

We'll start out thinking a bit like Douglas Adams in "The Restaurant at the End of the Universe", just to realize how mindbogginly big the universe really must be! I'm always awed at this point, we all are, actually, and see us the way we are. big in our own little universe, but infinetly small in the real one!

It's a small question with a big answer!

According to Big Bang proponents, if the Universe started as a pinprick of supercondensed material which then expanded in all directions from it's origin, then this material is still expanding today, in which case, it should have a boundary!

Yeah I agree a boundry seems reasonable but when it gets to it's outtermost limit at that point it's going to start coming back on us, I think that's part of of the bigbangers theory also.

Let's put a twist to this question:

If the "space" within our Universe is mostly vacuous, up to the point of the "boundary," then what is on the "other side" of the boundary?

Is it vacuous also? or is it full of anti-matter?

Let's put a twist to this question:

If the "space" within our Universe is mostly vacuous, up to the point of the "boundary," then what is on the "other side" of the boundary?

Is it vacuous also? or is it full of anti-matter?

I think this is what I was thinking earlier. Even if it's vacuous, it's still a part of the universe so it isn't an edge boundry to my way of thinking - it's just a part of the universe where nothing exists.. .

I think scientifically, the outer limit of the universe is where the first bits to eject from the big bang are now. I also think it mostly takes the form of infrared light.

We've only gotten back to about 25% the age of the universe (75% of the universe's history is unseen and unknown to us). But, one scientist states in an article in space.com that he thinks with new tech, we'll be able to see much farther within a few years.

Time and space were both created at the big bang, so they have no meaning outside the context of the big bang. We can't ask what is on the other side of the edge of the cosmos because the question doesn't have context anymore. We might as well ask, what is on the other side of time?

Yes- there is a limit to the cosmos. When we look into a telescope, we are seeing backward into time. Objects furthest away from us appear in the telescope as they did near the dawn of time. If we COULD look far enough in the sky (in any direction, take your pick) we could see the big bang, except that it predates light.

An easy proof that the cosmos is finite:
If infinite stars existed outward in time and space to infinity, we would be able to see their light, even as the tiniest of pinpricks in the night sky. The night should be a solid mass of light from an infinite number of stars and galaxies shining light toward us from infinite time. The night is NOT a solid mass of light. Therefore, the cosmos is finite.

Oh I see a time discussion coming. If the past is seeing backward, like in a telescope, then lets just turn it around. sorry - couldn't help myself.

Equus, so what your saying is that light does not lose it's energy to disapate into darkness? And your thinking that the earth shines or reflects light so.. better getting to rethinking on that one.. :-)
What about blackholes that suck up the light they do not radiate light, what about dark sides of planets not reflecting light?

## Does the UNIVERSE have a boundary or OUTER LIMIT?

can you explain this a little better please. I'm not following it.

In what medium does the balloon float?

That's a good question? If our universe is finite, like the balloon analogy suggests, what is outside our universe? I'd love to hear some physicists ideas on that. Does anyone have Stephen Hawking's email address?

1. nothing, our universe is all that there is (even though its finite)
2. Our universe is infinite (in which case there are major flaws with the balloon analogy)
Interesting quote: "If the universe is infinite, it would also contain an infinite amount of matter. In this case, literally every possible arrangement of matter is present an infinite number of times. There are an infinite number of Earths out there, if we look far enough afield, some drastically different from ours, some virtually identical, some literally identical. Actually, there would be an infinite number of every one of the infinite possible Earths. As to what’s outside this universe, well, there’s obviously nothing beyond an infinite border." Mind boggling.
3."then there are the multiverse explanations. These postulate that the universe split off after the Big Bang into everything from bubbles to sheets. Our universe is just one of many, possibly a finite number or possibly infinite. In this conception, what’s “outside” our universe is simply another universe. It could have identical physical laws to our own home, or have completely different ones. Everything from gravity to the strong nuclear force could be different, leading to a reality that could behave differently in fundamental ways"

-But then your question still has relevance what medium fills the space between these universes?

Cosmologists have the best jobs. They get paid to sit around and think about this crazy stuff. It makes me realize how much my job sucks. Sorry for the long reply.

## Contents

As stated in the introduction, there are two aspects to consider:

1. its local geometry, which predominantly concerns the curvature of the universe, particularly the observable universe, and
2. its global geometry, which concerns the topology of the universe as a whole.

The observable universe can be thought of as a sphere that extends outwards from any observation point for 46.5 billion light-years, going farther back in time and more redshifted the more distant away one looks. Ideally, one can continue to look back all the way to the Big Bang in practice, however, the farthest away one can look using light and other electromagnetic radiation is the cosmic microwave background (CMB), as anything past that was opaque. Experimental investigations show that the observable universe is very close to isotropic and homogeneous.

If the observable universe encompasses the entire universe, we may be able to determine the structure of the entire universe by observation. However, if the observable universe is smaller than the entire universe, our observations will be limited to only a part of the whole, and we may not be able to determine its global geometry through measurement. From experiments, it is possible to construct different mathematical models of the global geometry of the entire universe, all of which are consistent with current observational data thus it is currently unknown whether the observable universe is identical to the global universe, or is instead many orders of magnitude smaller. The universe may be small in some dimensions and not in others (analogous to the way a cuboid is longer in the dimension of length than it is in the dimensions of width and depth). To test whether a given mathematical model describes the universe accurately, scientists look for the model's novel implications—what are some phenomena in the universe that we have not yet observed, but that must exist if the model is correct—and they devise experiments to test whether those phenomena occur or not. For example, if the universe is a small closed loop, one would expect to see multiple images of an object in the sky, although not necessarily images of the same age.

Cosmologists normally work with a given space-like slice of spacetime called the comoving coordinates, the existence of a preferred set of which is possible and widely accepted in present-day physical cosmology. The section of spacetime that can be observed is the backward light cone (all points within the cosmic light horizon, given time to reach a given observer), while the related term Hubble volume can be used to describe either the past light cone or comoving space up to the surface of last scattering. To speak of "the shape of the universe (at a point in time)" is ontologically naive from the point of view of special relativity alone: due to the relativity of simultaneity we cannot speak of different points in space as being "at the same point in time" nor, therefore, of "the shape of the universe at a point in time". However, the comoving coordinates (if well-defined) provide a strict sense to those by using the time since the Big Bang (measured in the reference of CMB) as a distinguished universal time.

The curvature is a quantity describing how the geometry of a space differs locally from the one of the flat space. The curvature of any locally isotropic space (and hence of a locally isotropic universe) falls into one of the three following cases:

1. Zero curvature (flat) a drawn triangle's angles add up to 180° and the Pythagorean theorem holds such 3-dimensional space is locally modeled by Euclidean spaceE3 .
2. Positive curvature a drawn triangle's angles add up to more than 180° such 3-dimensional space is locally modeled by a region of a 3-sphereS3 .
3. Negative curvature a drawn triangle's angles add up to less than 180° such 3-dimensional space is locally modeled by a region of a hyperbolic spaceH3 .

Curved geometries are in the domain of Non-Euclidean geometry. An example of a positively curved space would be the surface of a sphere such as the Earth. A triangle drawn from the equator to a pole will have at least two angles equal 90°, which makes the sum of the 3 angles greater than 180°. An example of a negatively curved surface would be the shape of a saddle or mountain pass. A triangle drawn on a saddle surface will have the sum of the angles adding up to less than 180°.

General relativity explains that mass and energy bend the curvature of spacetime and is used to determine what curvature the universe has by using a value called the density parameter, represented with Omega ( Ω ). The density parameter is the average density of the universe divided by the critical energy density, that is, the mass energy needed for a universe to be flat. Put another way,

• If Ω = 1 , the universe is flat.
• If Ω > 1 , there is positive curvature.
• If Ω < 1 there is negative curvature.

One can experimentally calculate this Ω to determine the curvature two ways. One is to count up all the mass-energy in the universe and take its average density then divide that average by the critical energy density. Data from Wilkinson Microwave Anisotropy Probe (WMAP) as well as the Planck spacecraft give values for the three constituents of all the mass-energy in the universe – normal mass (baryonic matter and dark matter), relativistic particles (photons and neutrinos), and dark energy or the cosmological constant: [11] [12]

The actual value for critical density value is measured as ρcritical = 9.47×10 −27 kg m −3 . From these values, within experimental error, the universe seems to be flat.

Another way to measure Ω is to do so geometrically by measuring an angle across the observable universe. We can do this by using the CMB and measuring the power spectrum and temperature anisotropy. For instance, one can imagine finding a gas cloud that is not in thermal equilibrium due to being so large that light speed cannot propagate the thermal information. Knowing this propagation speed, we then know the size of the gas cloud as well as the distance to the gas cloud, we then have two sides of a triangle and can then determine the angles. Using a method similar to this, the BOOMERanG experiment has determined that the sum of the angles to 180° within experimental error, corresponding to an Ωtotal ≈ 1.00±0.12. [13]

These and other astronomical measurements constrain the spatial curvature to be very close to zero, although they do not constrain its sign. This means that although the local geometries of spacetime are generated by the theory of relativity based on spacetime intervals, we can approximate 3-space by the familiar Euclidean geometry.

The Friedmann–Lemaître–Robertson–Walker (FLRW) model using Friedmann equations is commonly used to model the universe. The FLRW model provides a curvature of the universe based on the mathematics of fluid dynamics, that is, modeling the matter within the universe as a perfect fluid. Although stars and structures of mass can be introduced into an "almost FLRW" model, a strictly FLRW model is used to approximate the local geometry of the observable universe. Another way of saying this is that if all forms of dark energy are ignored, then the curvature of the universe can be determined by measuring the average density of matter within it, assuming that all matter is evenly distributed (rather than the distortions caused by 'dense' objects such as galaxies). This assumption is justified by the observations that, while the universe is "weakly" inhomogeneous and anisotropic (see the large-scale structure of the cosmos), it is on average homogeneous and isotropic.

Global structure covers the geometry and the topology of the whole universe—both the observable universe and beyond. While the local geometry does not determine the global geometry completely, it does limit the possibilities, particularly a geometry of a constant curvature. The universe is often taken to be a geodesic manifold, free of topological defects relaxing either of these complicates the analysis considerably. A global geometry is a local geometry plus a topology. It follows that a topology alone does not give a global geometry: for instance, Euclidean 3-space and hyperbolic 3-space have the same topology but different global geometries.

As stated in the introduction, investigations within the study of the global structure of the universe include:

• whether the universe is infinite or finite in extent,
• whether the geometry of the global universe is flat, positively curved, or negatively curved, and,
• whether the topology is simply connected like a sphere or multiply connected, like a torus. [14]

### Infinite or finite Edit

One of the presently unanswered questions about the universe is whether it is infinite or finite in extent. For intuition, it can be understood that a finite universe has a finite volume that, for example, could be in theory filled up with a finite amount of material, while an infinite universe is unbounded and no numerical volume could possibly fill it. Mathematically, the question of whether the universe is infinite or finite is referred to as boundedness. An infinite universe (unbounded metric space) means that there are points arbitrarily far apart: for any distance d , there are points that are of a distance at least d apart. A finite universe is a bounded metric space, where there is some distance d such that all points are within distance d of each other. The smallest such d is called the diameter of the universe, in which case the universe has a well-defined "volume" or "scale."

#### With or without boundary Edit

Assuming a finite universe, the universe can either have an edge or no edge. Many finite mathematical spaces, e.g., a disc, have an edge or boundary. Spaces that have an edge are difficult to treat, both conceptually and mathematically. Namely, it is very difficult to state what would happen at the edge of such a universe. For this reason, spaces that have an edge are typically excluded from consideration.

However, there exist many finite spaces, such as the 3-sphere and 3-torus, which have no edges. Mathematically, these spaces are referred to as being compact without boundary. The term compact means that it is finite in extent ("bounded") and complete. The term "without boundary" means that the space has no edges. Moreover, so that calculus can be applied, the universe is typically assumed to be a differentiable manifold. A mathematical object that possesses all these properties, compact without boundary and differentiable, is termed a closed manifold. The 3-sphere and 3-torus are both closed manifolds.

### Curvature Edit

The curvature of the universe places constraints on the topology. If the spatial geometry is spherical, i.e., possess positive curvature, the topology is compact. For a flat (zero curvature) or a hyperbolic (negative curvature) spatial geometry, the topology can be either compact or infinite. [15] Many textbooks erroneously state that a flat universe implies an infinite universe however, the correct statement is that a flat universe that is also simply connected implies an infinite universe. [15] For example, Euclidean space is flat, simply connected, and infinite, but the torus is flat, multiply connected, finite, and compact.

In general, local to global theorems in Riemannian geometry relate the local geometry to the global geometry. If the local geometry has constant curvature, the global geometry is very constrained, as described in Thurston geometries.

The latest research shows that even the most powerful future experiments (like the SKA) will not be able to distinguish between flat, open and closed universe if the true value of cosmological curvature parameter is smaller than 10 −4 . If the true value of the cosmological curvature parameter is larger than 10 −3 we will be able to distinguish between these three models even now. [16]

Results of the Planck mission released in 2015 show the cosmological curvature parameter, ΩK, to be 0.000±0.005, consistent with a flat universe. [17]

#### Universe with zero curvature Edit

In a universe with zero curvature, the local geometry is flat. The most obvious global structure is that of Euclidean space, which is infinite in extent. Flat universes that are finite in extent include the torus and Klein bottle. Moreover, in three dimensions, there are 10 finite closed flat 3-manifolds, of which 6 are orientable and 4 are non-orientable. These are the Bieberbach manifolds. The most familiar is the aforementioned 3-torus universe.

In the absence of dark energy, a flat universe expands forever but at a continually decelerating rate, with expansion asymptotically approaching zero. With dark energy, the expansion rate of the universe initially slows down, due to the effect of gravity, but eventually increases. The ultimate fate of the universe is the same as that of an open universe.

#### Universe with positive curvature Edit

A positively curved universe is described by elliptic geometry, and can be thought of as a three-dimensional hypersphere, or some other spherical 3-manifold (such as the Poincaré dodecahedral space), all of which are quotients of the 3-sphere.

Poincaré dodecahedral space is a positively curved space, colloquially described as "soccerball-shaped", as it is the quotient of the 3-sphere by the binary icosahedral group, which is very close to icosahedral symmetry, the symmetry of a soccer ball. This was proposed by Jean-Pierre Luminet and colleagues in 2003 [8] [18] and an optimal orientation on the sky for the model was estimated in 2008. [9]

#### Universe with negative curvature Edit

A hyperbolic universe, one of a negative spatial curvature, is described by hyperbolic geometry, and can be thought of locally as a three-dimensional analog of an infinitely extended saddle shape. There are a great variety of hyperbolic 3-manifolds, and their classification is not completely understood. Those of finite volume can be understood via the Mostow rigidity theorem. For hyperbolic local geometry, many of the possible three-dimensional spaces are informally called "horn topologies", so called because of the shape of the pseudosphere, a canonical model of hyperbolic geometry. An example is the Picard horn, a negatively curved space, colloquially described as "funnel-shaped". [10]

#### Curvature: open or closed Edit

When cosmologists speak of the universe as being "open" or "closed", they most commonly are referring to whether the curvature is negative or positive. These meanings of open and closed are different from the mathematical meaning of open and closed used for sets in topological spaces and for the mathematical meaning of open and closed manifolds, which gives rise to ambiguity and confusion. In mathematics, there are definitions for a closed manifold (i.e., compact without boundary) and open manifold (i.e., one that is not compact and without boundary). A "closed universe" is necessarily a closed manifold. An "open universe" can be either a closed or open manifold. For example, in the Friedmann–Lemaître–Robertson–Walker (FLRW) model the universe is considered to be without boundaries, in which case "compact universe" could describe a universe that is a closed manifold.

#### Milne model (hyperbolic expanding) Edit

If one applies Minkowski space-based special relativity to expansion of the universe, without resorting to the concept of a curved spacetime, then one obtains the Milne model. Any spatial section of the universe of a constant age (the proper time elapsed from the Big Bang) will have a negative curvature this is merely a pseudo-Euclidean geometric fact analogous to one that concentric spheres in the flat Euclidean space are nevertheless curved. Spatial geometry of this model is an unbounded hyperbolic space. The entire universe in this model can be modelled by embedding it in Minkowski spacetime, in which case the universe is included inside a future light cone of a Minkowski spacetime. The Milne model in this case is the future interior of the light cone and the light cone itself is the Big Bang.

For any given moment t > 0 of coordinate time within the Milne model (assuming the Big Bang has t = 0 ), any cross-section of the universe at constant t' in the Minkowski spacetime is bounded by a sphere of radius c t = c t' . The apparent paradox of an infinite universe "contained" within a sphere is an effect of the mismatch between coordinate systems of the Milne model and the Minkowski spacetime in which it is embedded.

This model is essentially a degenerate FLRW for Ω = 0 . It is incompatible with observations that definitely rule out such a large negative spatial curvature. However, as a background in which gravitational fields (or gravitons) can operate, due to diffeomorphism invariance, the space on the macroscopic scale, is equivalent to any other (open) solution of Einstein's field equations.