If the universe is infinite then it wasn't a single point, when physicists talk about a "Single point" they usually refer to the "Observable universe" which is finite. in fact when they talk about the "Universe" they usually just mean the observable part.

If the universe as a whole(including outside of the observable universe) then it wasn't a single point, infinite was always infinite and will always be infinite.

The leading idea is that there's no single point but every point in the universe is the center of big bang, a finite volume of space comes from a point and every point expands into a finite volume the size of the observable universe.

If the universe is spatially flat and can still be finite.

The surface of the torus (donut) can also be spatially flat, but it is finite. So you have two possibilities for a flat Universe: one infinite, like a plane, and one finite, like a torus, where both are flat.

Be careful, technically a torus is not flat at most points when drawn as a donut. One needs to use the "flat torus" which can only be properly embedded ("drawn") in 4 dimensions.

To add to this though, Not all tori are flat. Donut isn't flat it's negative on the inside and positive on the outside. When we specifically talk about tori that are flat, we usually refer to them as "flat torus"

> If the universe as a whole(including outside of the observable universe) then it wasn't a single point, infinite was always infinite and will always be infinite.

This misconception is weirdly common and contradicts basic topology:

If every bubble of, say, 10^10 ly, was once a single point, then the entire universe was once a single point.

Proof: assume x,y are any two points. Connect them by a path of finite (but potentially extremely large, even by universe standards) length. Overlay that path with finitely many of those 10^10 ly bubbles, such that they overlap, forming a "chain". Let A, B be two neighboring overlapping bubbles. Then once all points of A were the same point a, and all of B were once the same point b. But now look at any point p in their intersection: p was once both a and b, thus a=b! Doing this iteratively with the chain of bubbles, we arrive at the conclusion that any two points were once the same! [ ]

And indeed, the infinite(!) 3D (or 4D) space is contractible, it can be contracted into a single point in finite time. Even at locally finite & bounded speed.

Anyway, there are quite a few models of the Big Bang where the universe was always infinite, just with also infinite density at the beginning. The Big Bang needs not necessarily be a single point in the usual sense.

So flat does not equal infinite. One option is an infinite universe but there are finite options that are flat in their fundamental domain. The universe has a topology. The part we care about is curvature. Lets drop one spacial dimension. So now the universe could be something like the surface of a sphere it has positive curvature. The defining property of positive curvature is that initially parallel lines converge and the opposite for negative curvature. Now flat topology is where parallel lines remain parallel.

Lets look at an example you got a 2D universe with flat geometry. Its a sheat of paper. One option is that the paper is infinite. Parallel lines on that paper remain parallel. This is the geometry in the fundamental domain (2D) of this universe. Now lets give it a rule, lines going far enough to the left emerge on the right coming back to their start. If you want to embed this topology in 3D you just connect the left and right edge. You got a cylinder. It has flat geometry in its fundamental domain and is almost finite. To make it finite we connect the upper and lower edge to get a torus a donut. It has a flat geometry and a finite size, you go far enough in any direction you get back where you started. As it turns out you can embed a this flat geometry and get a torus without distortions. So add an extra dimension with the same rules and our 3D universe could be though of as the surface of a 4D torus. But there are other options that also have a flat geometry in their fundamental domain but give us a finite universe.

For an infinite universe it has always been infinite. The big bag happened everywhere. You being able to trace back every path to a single point only means that the universe is scale invariant so you can resale it all you want. Lets look at density if you look at the universe now but zoom way out because volume essentially means nothing you see a really high matter density. So your scale for volume is arbitrarily. If you have a collection of points on a grid you can zoom in and conclude that the points have a low density but zoom out and see that they have a high density. If the universe is infinite you can pick an arbitrarily large scale and there is always a scale where the universe looks the same. Infinite means that you have no reference points for scale, there is no true scale to the universe. Well the only problem is matter being finitely divisible so something like the size of an atom kinda gives a scale to the universe. But the thing is an infinite universe is consistent with the data we have.

And yes infinite energy is a consequence. And infinite density only means that the volume you pick is arbitrarily. Scale it up and density grows approaching infinite scale it down and it approaches 0.

And flattenes from the CMB is basically just draw a triangle as big as you can, so the two other points on the CMB is the largest we can make. Add up the angles, if its <180° thats negative curvature if ist >180° positive curvature and =180° means flat geometry.

So all in all you can think like this the global properties of the universe don't change. It always has an infinite density and an infinite size, but local properties can. You have a numberline with all the natural numbers. You can stretch the nubers and create larger gaps, the length of the numberline and the amount of stuff it contains remains and you can zoom out to get back the original "number density".

1-2-3-4-... early universe

1---2---3---4---... current universe zoom out and you see

1-2-3-4-... again.

Zoom out even further and everything overlaps.

● - you pretty much see a point.

There is a short answer to your title question: "nobody knows and currently have no way of knowing". Any contradictions come from comparing ideas that aren't meant to go together because they're parts of different models.

We don't know if the universe is infinite. We don't know what was happening at the earliest moments of the universe. Was it a single point? Maybe, although that's a very unpopular idea among physicists, just like the singularity in black holes. It contradicts quantum mechanics. There's currently not a better model, but they're pretty certain infinite density should be false.

We simply do not have the maths or technology to answer those questions. It would require the "Theory of Everything", with quantum gravity and all that. And the tech to test it.

To the followup questions.

It's absolutely possible for infinite space to have infinite matter and still be relatively "empty". There's just more space than matter. Just repeat what you can see in the sky infinitely in all directions. There's no contradiction.

Expansion can be weird to think about, but that's why the baloon/rubber band imagery is helpful. If every point in space stretches the same amount, something 1 "unit" away will stretch to 2, but 2 will stretch to 4. So distance matters. "Our local area" is the few neighbouring galaxies that are gravitationally bound, so any expansion of space (at observed rates) that close wouldn't be significant.

Also, expansion isn't actually uniform, gravity does counteract it. There is no expansion within a galaxy, or even within clusters (as far as I understand). The concentration of mass counteracts expansion.

BTW, our immediate vicinity being fairly empty actually IS weird. Our galaxy is actually in a void, imaginatively called the Local Void. The galactic neighbourhoods are usually more busy.

As for CMB and flatness, I only have a rough idea based on what I've read, but essentially is goes like this: "flatness" of soacetime is all about parallel lines being parallel and angles in a triangle adding up to 180 degrees. So geometry you'd do on a sheet of paper. For example, on the surface of the earth which is NOT flat, you can draw three lines (along the great circles) which will meet at 90 degrees and yet form a triangle. That's non-euclidian geometry.

Where the CMB comes in is the fact that it represents the very early universe. But it directly corresponds to today's universe, but everything has grown since then. So depending on the curvature of the universe, the patterns in the CMB should have specific shapes, corresponding to the massive structures in the visible universe. So astronomers made the observations, made the modelling, and the shape of the CMBs patters corresponds to the model where spacetime is flat.

Thank you for the detailed response! I am hoping we can at least get some answers toward a unified theory soon, hopefully in my lifetime lol

You are assuming that the universal speed limit, aka. the speed of light, applies to space itself. But this is not the case. Nothing can move faster then the univerals speed limit compared to the fabric of spacetime but the fabric itself does move faster then this. As far as we can tell the space that is infinatly far away from us also have infinate speed away from us. It could therefore have moved from a single point to where it is now.

That's pretty interesting, hadnt thought about the unique geometries that allow flatness but still are unbounded. There doesn't appear to be any reason it would be a torus but I suppose there is no reason for it to be any shape, it just is whatever shape it is.

Tying to understand these concepts in a human mind is dizzying sometimes. I hope I can stay the course and continue studying and eventually join the effort to answer these questions

I'm catiously optimistic

From an observer's point of view, the universe grows at the speed of light since the Big Bang if it's flat. It's always finite. The boundary doesn't age, so it's still at the Big Bang with an infinite density.

From a global point of view, a flat universe went from a volume of 0 to an infinite volume instantly at the Big Bang. The universe contains matter that goes from a speed of 0 to infinity, and it can go from a volume of 0 to infinity instantly. The speed between each piece of matter is proportional to its distance.

The speed in the global point of view is equal to gamma*the speed in the observer's point of view. So a speed of c for an observer is equal to a speed of infinity globally as gamma is infinite for v=c.

Conversely, I have heard arguments that the misconception was that any part of the universe, infinite or otherwise, was a single point. Rather, all points were infinitesimally close, but not occupying the same space and not truly one point. In that case, the universe would continue to be infinitely large and infinitesimally small.

But I don't know enough about math or physics to know or argue one way or another.

It can't. People still argue over this today because they're not willing to admit that its just not possible. Matter cannot be created or destroyed. Evolution is not possible. It was God who did it all.

>Even at locally finite & bounded speed. >

How would that work? It seems like in the actual transition from a point into a space, speed wouldn't even be definable. Is there an explicit construction of such a contraction?

Please read this entire message

Your submission has been removed for the following reason(s):

Loaded questions are not allowed on ELI5. A loaded question is one that posits a specific view of reality and asks for explanations that confirm it. A loaded question, by definition, presumes that something must be true in order for the question to stand.

If you would like this removal reviewed, please read the detailed rules first. If you believe this submission was removed erroneously, please use this form and we will review your submission.

There are ways to work with infinitesimal numbers just as with real numbers, but that does not really do the trick, as physics is not based on that. To my understanding (not an expert in cosmology or that deep into physics) the energies/fields of back then can cause infinite densities.

If inside the same space:

Let t be a real number running from 0 to a(ge of universe). We contract space to a point inside itself by sending each vector v at time t to (a-t)·v. So at t=0, v is wherever it should be, and at t=a we get 0 (italic to denote it is the vector 0, not the number 0) regardless of v. And in-between, it moves towards that inevitable 0.

This does not "jump" (it is continuous), but from an external view, v does move with speed |v|/a (with |v| the distance of v from 0) all the time. So points far away move arbitrarily fast, similar to how some parts of the universe move away from us faster than the speed of light. But "locally", so if every point only observes those close to it, points have almost the same speed and direction. So within a close bubble, the rest of space moves only slowly.

Now we have the issue that the real universe is not contracting/expanding "within itself". This requires some slight fixes and makes the calculations a bit more ugly (hence why I did the above first):

One should think about the universe at each time t as its separate thing: imagine the Universe as a planar flat thing; now draw a time-scale in another dimension (so we need 4D if we do the real thing); lastly, fix a random point B ("Big Bang") at distance a from U and draw all the "rays" starting in B towards each point of the universe.

If U were a perfect circle, this gives you an actual cone, and this is indeed called the cone construction. Whatever U was though, one can now contract towards B in this cone(ish) thing we made as before.

Now that is still pretty far from what General relativity tells us, but I hope it explains how one can model such a thing.