Big Bang: Size of the Universe at Different Epochs

[KingGambit]

TL;DR Summary

The size of the universe after
Inflationary epoch
Quark epoch
Baryogenesis
Photon epoch

Dear PF Forum,

I've been searching what was the size of the early univese, but I think I might have hit the wall.
I read that in the end of inflationary epoch, 10^-32 seconds, the size of the universe was as big as a grape fruit?
And after that, it seems that I can't find a reference to the size of the universe.
For example in Baryogenesis epoch, 10^-11 seconds, if all atoms were created at that point, then what was the size of the universe then?
The mass of the Observable Universe is about... 10²³ solar mass. And we know that an average neutron star (1.5 solar mass) size is 20 km in diameter. I know this is wrong if I am to extrapolate that number, the size of the universe at around Baryogenesis would be... 10⁷ solar diameter or about 1 light year? I know this is completely wrong.
I am wondering if someone can help me with the size of the universe at
- Quark epoch (10^-5 seconds)
- Photon epoch (380,000 years)

Thank you very much.

I have read this:
https://en.wikipedia.org/wiki/Chronology_of_the_universe
But I found no information about the size of the universe.

 

[anorlunda]

I read that in the end of inflationary epoch, 10-32 seconds, the size of the universe was as big as a grape fruit?

You made a very common mistake missing one key word.

"in the end of inflationary epoch, 10-32 seconds, the size of the visible universe was as big as a grape fruit"

The visible universe is the portion that we can see. The entire universe is believed to be infinite in size today. Therefore it must have been infinite in size before the big bang.

This PF Insights article may help you.
https://www.physicsforums.com/insights/brief-expansion-universe/

 

[kimbyd]

Nit: we don't and can't know if the universe is infinite. But it's generally expected to be at least much larger than the observable portion that was the size of a grapefruit in that early epoch.

 

[pinball1970]

Nit: we don't and can't know if the universe is infinite. But it's generally expected to be at least much larger than the observable portion that was the size of a grapefruit in that early epoch.

I have read a few threads on this and when one comes round I always try and think and see if I am understanding what is being said.

It is thought the whole universe is infinite in size and always has been, it is not thought to be temporally infinite yes?

The observable universe began very small hot and dense and expanded.

So a question.

Was the region “outside” our part, the infinite part, also thought to be in the same/similar condition?

So if I could travel beyond the observable universe I would find more of the same? Galaxies with stars?

Or is this not really discussed that much since it can never be detected? Not science?

Also if there are threads/insights I should read on pf? Specifically on this

There are lots of posts like this https://www.physicsforums.com/threa...rse-and-infinity-according-to-physics.639254/

I would like a recent, relevant one if poss. Thanks

 

[Drakkith]

It is thought the whole universe is infinite in size and always has been, it is not thought to be temporally infinite yes?

It is unknown whether the universe has existed in some form for an infinite or finite amount of time. Our models predict a t=0, but only because that's when the math breaks down and we get a singularity. It is entirely possible this is an artifact of our incomplete knowledge of physics at the extremely high energy and density ranges found during this period.

It's also thought that the universe is infinite in size. Mainly because we haven't seen an edge or boundary and because these things are somewhat problematic to have in any model. Oddly enough, the simplest model is one where the universe is infinite in size, as it doesn't require any of the special shapes or conditions that the universe must have in order to be spatially finite.

The observable universe began very small hot and dense and expanded.

That's right.

Was the region “outside” our part, the infinite part, also thought to be in the same/similar condition?

Yes. The entire universe is presumed to have been in a near-identical state.

So if I could travel beyond the observable universe I would find more of the same? Galaxies with stars?

That is correct.

 

[Ibix]

Was the region “outside” our part, the infinite part, also thought to be in the same/similar condition?

The FLRW cosmological model says the universe can be infinite in extent and pretty much the same everywhere, or it can be finite and closed (like the surface of a sphere - finite area but no edges). Observations match the universe being infinite in extent to our best precision, but we can't rule out a REALLY big closed universe, so big our entire observable universe is like your kitchen floor compared to the Earth.

Either way, we predict everything to be more or less the same everywhere even in the bits we can't see - but we can't actually go and check.

 

[anorlunda]

it is not thought to be temporally infinite yes?

If you think it through, it is not possible for anything (universe or not universe) to grow from finite size to infinite size. To do so would require infinite speed of growth. So the word temporary can not be paired with finite or infinite.

 

[pinball1970]

If you think it through, it is not possible for anything (universe or not universe) to grow from finite size to infinite size. To do so would require infinite speed of growth. So the word temporary can not be paired with finite or infinite.

I put temporally not temporary.

I had never thought about this till reading about the subject on pf (within the last year possibly) and yes it makes sense.

If it is infinite now it always had to be and always will be (what if an finite volume expanded for an infinite amount of time? Joke)

One thing I cannot understand is how an infinite volume of space now could have a finite past?

That to me says there was an infinity at the beginning of time, apart from the fact that sounds like a Yes album, that completely blows my mind.

 

[Ibix]

One thing I cannot understand is how an infinite volume of space now could have a finite past?

In a vanilla FLRW model, the scale factor goes to zero 14bn years ago, which means that all points in space are distinct but the distance between any of them is zero. That's the Big Bang singularity. We don't like it because it's exactly as contradictory as it sounds. More modern models get rid of the singularity, and I think (and I'm sure @PeterDonis will correct me if I'm wrong) that they give an infinite past to spacetime.

 

[PeterDonis]

More modern models get rid of the singularity

Some do, and some don't. Whether or not there is a past singularity in our actual universe is still an open question.

 

[PeterDonis]

the scale factor goes to zero 14bn years ago, which means that all points in space are distinct but the distance between any of them is zero. That's the Big Bang singularity. We don't like it because it's exactly as contradictory as it sounds.

Strictly speaking, the singularity itself is not part of spacetime, so there is no actual part of spacetime where the contradictory-sounding thing is true. However, it is still true that you can only go a finite time into the past along any past-directed timelike or null geodesic if there is a past singularity, and many physicists believe that is not physically reasonable--that any geodesic should be extendible indefinitely. That is why many physicists believe that the presence of a singularity in a model is a signal that the model breaks down in that regime, and that we will need some better model, possibly using a more comprehensive theory (such as quantum gravity), for that regime.

 

[phinds]

I put temporally not temporary.

Ha. I also read it as temporarily.

 

[pinball1970]

Ha. I also read it as temporarily.

Good catch!

I could have said, 'please credit me with at least some intelligence,' but that's a bit of an ask on pf isn't it?
Vanadium would say. 'compared to what?'

@anorlunda scan read I think. Fair play, I'm asking basics

 

[anorlunda]

In a vanilla FLRW model, the scale factor goes to zero 14bn years ago, which means that all points in space are distinct but the distance between any of them is zero.

Is that true in the limit? If two points are infinitely far apart in space, does the distance between them approach zero as the scale factor approaches zero? I think not. GR is not needed, it's just the definition of infinity.

 

[Ibix]

Is that true in the limit? If two points are infinitely far apart in space, does the distance between them approach zero as the scale factor approaches zero? I think not. GR is not needed, it's just the definition of infinity.

I don't think you can really discuss it. As Peter reminds me, a singularity is not part of spacetime so it's not clear that "distance between points" makes sense since that's a notion provided by the metric of spacetime which the singularity isn't in. I was trying to express that the singularity is a mathematical self-contradiction and I think I probably over-stepped what you can say about it.

 

[kimbyd]

Whether the universe is infinite in space or not is, in my view, a distraction. The spatial infinity that exists in most cosmological models is a simplification: it's there not because it may or may not reflect reality, but because it's easier to write the equations.

What you should read that infinity as actually meaning about our universe is that it's big enough that its size is likely irrelevant to any observations we might make. Certainly this is the case so far: no observations to date have shown a hint of a finite size. That means the actual size is really really big. How big? Nobody knows.

I don't think it will ever be possible to conclude that the universe is infinite in space, as our observations will always be finite.

 

[pinball1970]

Whether the universe is infinite in space or not is, in my view, a distraction. The spatial infinity that exists in most cosmological models is a simplification: it's there not because it may or may not reflect reality, but because it's easier to write the equations.

What you should read that infinity as actually meaning about our universe is that it's big enough that its size is likely irrelevant to any observations we might make. Certainly this is the case so far: no observations to date have shown a hint of a finite size. That means the actual size is really really big. How big? Nobody knows.

I don't think it will ever be possible to conclude that the universe is infinite in space, as our observations will always be finite.

Does the infinite volume help with the flatness problem?
Measurements look flat because the volumes are so huge?
Also should the flatness look flatter as time goes on? The larger a sphere (for example) becomes the flatter the region you happen to be in looks? Geometrically?

 

[jbriggs444]

Is that true in the limit? If two points are infinitely far apart in space,

The assumption that the universe is spatially infinite does not entail the existence of two points with infinite separation.

 

[DaveC426913]

I don't get how to reconcile these two ideas:
- the universe may be infinite in size
- the observable universe grew from a very small volume to a very large volume without having a centre.

If the universe is/was infinite in size, and our observable universe was once a very small volume in that universe, then does that not mean the observable universe was/is in a specific location? That makes one pat of the universe special.

I've always thought that the BB spawned a universe that was closed - if you go in any direction for long enough, you will end up back where you started - which is how I can see the idea that there is no centre (or everywhere is the centre). The BB cannot have occurred an as expansion in space because there's nowhere you could have stood outside it and meausre any distance - all locations are within the volume of the expanding BB.

I guess my model of the universe is egregiously outdated now.

 

[jbriggs444]

If the universe is/was infinite in size, and our observable universe was once a very small volume in that universe, then does that not mean the observable universe was/is in a specific location? That makes one pat of the universe special.

We are at the center of our observable universe. Some alien 22 billion light years away is at the center of his. Neither location is special.

 

[phinds]

I don't get how to reconcile these two ideas:
- the universe may be infinite in size
- the observable universe grew from a very small volume to a very large volume without having a centre.

There is nothing remotely contradictory in those two statements EXCEPT that you have misrepresented the observable universe as not having a center. It has and always has had. It's exactly at your left eyeball when your right eye is closed. It's the UNIVERSE, not the observable universe, that has no center.

EDIT: And, yes, I have a different observable universe than you do (but not by much in the overall scheme of things)

 

[phinds]

The BB cannot have occurred an as expansion in space

Exactly. The BB was an expansion OF space, not IN space. The universe does not exist inside anything, it's all there is.

 

[PeterDonis]

I've always thought that the BB spawned a universe that was closed

This is one possibility, but our best current model says it is unlikely.

which is how I can see the idea that there is no centre (or everywhere is the centre)

This will be true in any homogeneous space, which is to say any space with constant curvature. The 3-sphere (constant positive curvature, closed) is one possibility, but not the only one. The other two are infinite flat space (zero curvature) and infinite hyperbolic space (constant negative curvature).

there's nowhere you could have stood outside it and meausre any distance

This is true whether the universe is spatially closed or not.

 

[DaveC426913]

We are at the center of our observable universe. Some alien 22 billion light years away is at the center of his. Neither location is special.

Yes. Of course.
I think I may have derailed my own idea, talking about the observable universe. Made a fool of myself.
Let's drop the observable universe component completely.So: does the hypothesis of an infinite universe still reconcile with a universe that expanded from a small, dense volume? How?

 

[KingGambit]

You made a very common mistake missing one key word.

"in the end of inflationary epoch, 10-32 seconds, the size of the visible universe was as big as a grape fruit"

The visible universe is the portion that we can see. The entire universe is believed to be infinite in size today. Therefore it must have been infinite in size before the big bang.

This PF Insights article may help you.
https://www.physicsforums.com/insights/brief-expansion-universe/

Yess..., the observable universe. I miss that word. I just realized the day after I post this question.
Thank you very much.

 

[KingGambit]

Thanks for all responses.
I really appreciate it.

 

[Drakkith]

So: does the hypothesis of an infinite universe still reconcile with a universe that expanded from a small, dense volume? How?

No, but that's not what happened. If our universe is infinite in size then the volume was never small. It was simply more dense in the past.

 

[OCR]

Made a fool of myself.

If our universe is infinite in size then the volume was never small.

And. . . light travels faster than sound.

This is why some people appear bright until they speak. . . . . Lol. . . . j/k .

.

 

[PeroK]

So: does the hypothesis of an infinite universe still reconcile with a universe that expanded from a small, dense volume? How?

A simple mathematical analogy is to consider the one-dimensional number line, with the integers (postive and negative) one unit apart. Now, imagine the effect of $f(n) = 2n$ for any integer $n$. Each number is now twice the distance from any other number than it was originally.

Note that although we might imagine $0$ at the centre of the number line, geometrically the number line looks the same from any position, so there is no geometric centre.

To take this analogy further, we could imagine a "time" parameter $t$ and the function: $f(n, t) = tn$. At time $t = 1$ we have the regular number line. At time $t > 1$, the number lines expands. And, as we run the time parameter back towards $t = 0$, the integer points become more dense. Note that at any finite time $t$ we have an infinite number line with finite density. For $t > 0$ this process is fully reversible.

If, however,we try $t = 0$, we have all integers mapped to a single point. The number line has gone and we have a singularity. Not least, because there is now no inverse process to get us from a single point to an infinite number line.

 

[anorlunda]

The assumption that the universe is spatially infinite does not entail the existence of two points with infinite separation.

Uh oh. That, I don't understand. Because of curvature? Where can I learn about that?

 

[PeroK]

Uh oh. That, I don't understand. Because of curvature? Where can I learn about that?

The number line is infinite, but the difference of any two numbers is finite.

There's a difference between saying that an integer can be arbitrarily large and saying that an integer can be infinite.

 

[jbriggs444]

The assumption that the universe is spatially infinite does not entail the existence of two points with infinite separation.

Uh oh. That, I don't understand. Because of curvature? Where can I learn about that?

It is a bit of pure mathematics. It sounds contradictory but it isn't. It may require adjusting your intuition of what is meant by an infinite set.

[It took a week for me to grasp and wrap an intuition around. It was second year of University and we were being exposed to an axiomatic description of the natural numbers using the Peano axioms]

The example given by @PeroK (the number line populated with integers) is very much on point.

So you have this number line. Every position on the number line corresponds to a finite integer. But there are infinitely many such positions. It is tempting to try to weasel out by considering the number line as some sort of incomplete process or potential infinity. But you need to accept it as a completed whole.

That is an uncomfortable intuition. But can you find an actual contradiction? Can you explain that apparent contradiction clearly enough that we can discuss it?

 

[DaveC426913]

No, but that's not what happened. If our universe is infinite in size then the volume was never small. It was simply more dense in the past.

Ah. Got it. PeroK's number line analogy helps.

 

[pinball1970]

The assumption that the universe is spatially infinite does not entail the existence of two points with infinite separation.

Even if it is flat?

Using the number line analogy what about plus and minus infinity?

If plus and minus infinity can be a physical thing then points in those places should also be infinitely apart?

If they are not infinitely apart because the number line is a concept rather than a physical thing then how can the physical universe be infinite?

 

[jbriggs444]

Using the number line analogy what about plus and minus infinity?

Neither are positions on the number line.