Radius and Size of the universe

[Rocketjj]

Hello,

I have read a lot of different articles about the estimated size of the universe, however there seems to be a lot of different theories. Most of the articles I have read have been a little dated, so I was wondering what's the current best guess.

I know the universe is around 13.7 billion years old. I can understand that the radius of the universe could be = age of universe X speed of light (Nothing can travel faster than a photon of light, right?)

I then read an article which said this was false. As the universe is expanding, the area behind this traveling photon would have increased, making the radius about 3 times the distance of the above. Other suggestions were that it was infinite in size

I just want a rough idea as to the radius of the universe really, just to give a brief 1-2 paragraph introduction to a research paper I am writing. If anyone has a link or the name of an up to date article it would be great. Any help is appreciated, Thank you
Mike

 

[mgb_phys]

I know the universe is around 13.7 billion years old. I can understand that the radius of the universe could be = age of universe X speed of light (Nothing can travel faster than a photon of light, right?)

That is false - the universe can expand faster than the speed of light (that's not the same as something traveling faster than light!)
A rough estimate the observable universe - that is the distance to the most distant observable things has a radius of around 45Bn lyr.
What happened was that light left them when they were much closer to us and the space between us expanded over the last 14Bn yr.
So a sphere with diameter of 90-95Bn lyr is a defensible one line explanation,.

How big the total universe depends on your cosmological model, especially if you start to believe in multiverses etc.
Many people prefer to only talk in concrete terms about the observable universe an leave all the rest to the mathematicians and philosophers of science.

 

[Rocketjj]

Thanks for the reply

Can I just check I understand what you said.

-If a ray of light that reaches Earth is 14billion LYs old (lets say). The source of this light is now much further than 14billion light years away due to the expanding universe?

-Is the whole universe expanding, or just certain parts. Wouldn't this imply that we are getting further and further away from other galaxies, planets etc? or does gravity keeps things in place

-The observable universe. Is that basically a model, where you take into account what you are actually seeing at that moment in time, rather than what state the universe is actually in? is there any chance you could direct me to an article showing the deduction of a 45billion light year radius?

Many thanks, sorry for all the questions. It's all quite confusing!

 

[mgb_phys]

-If a ray of light that reaches Earth is 14billion LYs old (lets say). The source of this light is now much further than 14billion light years away due to the expanding universe?

Yep - the CMB is the most distant object we can see, the light left it just when light and matter stopped being the same thing, about 380,000 years after the start. It's been traveling to usfor 14Bn lyr

-Is the whole universe expanding, or just certain parts.

That gets a bit philosophical, but I would say that our bit isn't special so it all is.

Wouldn't this imply that we are getting further and further away from other galaxies, planets etc? or does gravity keeps things in place

On large scales expansion is important, on small scales (upto clusters of galaxies size!) gravity wins.

-The observable universe. Is that basically a model, where you take into account what you are actually seeing at that moment in time, rather than what state the universe is actually in?

It's a model based on the expansion rate, the 4d shape of space time and the age of the universe

is there any chance you could direct me to an article showing the deduction of a 45billion light year radius?

Not that I know of - I don't really work in this area.
Marcus (https://www.physicsforums.com/member.php?u=66) is the expert on this, you could pm him if he doesn't see this thread.

Many thanks, sorry for all the questions. It's all quite confusing!

The universe confusing? really ;-)

 

[marcus]

Hello,

I have read a lot of different articles about the estimated size of the universe, however there seems to be a lot of different theories. Most of the articles I have read have been a little dated, so I was wondering what's the current best guess.

I know the universe is around 13.7 billion years old. I can understand that the radius of the universe could be = age of universe X speed of light (Nothing can travel faster than a photon of light, right?)

I then read an article which said this was false. As the universe is expanding, the area behind this traveling photon would have increased, making the radius about 3 times the distance of the above. Other suggestions were that it was infinite in size

I just want a rough idea as to the radius of the universe really, just to give a brief 1-2 paragraph introduction to a research paper I am writing. If anyone has a link or the name of an up to date article it would be great. Any help is appreciated, Thank you
Mike

Size of universe is a cosmology question. If you have more cosmo questions you may get more response if you post in Cosmo forum. In this case Mgb already answered regarding the current distance to the matter which emitted the CMB. I agree with Mgb about this: 45 or 46 billion LY.

That is not what cosmologists (the ones I know anyway ) call "the size of the universe." They make a clear distinction between the size of the universe and the farthest we can currently see (the radius of the observable part). I don't know what information you want to put in your paper.

Is it current estimates of the size of the whole universe? Or just the size of the observable chunk? Or both?

Do you want a volume estimate, a mass estimate, a radius estimate, or all three?

A recent paper with lots of up-to-date estimates is Komatsu et al (2008)
http://arxiv.org/abs/0803.0547
It's kind of dense, packed with information, not easy to read. But it is the latest most authoritative source I know, about cosmology parameters.

We can find stuff in the paper and interpret for you if you say what you want to know---what information you want for the paper you are writing.

 

[marcus]

I might as well tell you some stuff rather than waiting for you to say exactly what would be right for your paper.
Komatsu et al is the official blue-ribbon report from nasa's WMAP orbital observatory, the 5-year data, as it relates to cosmology. Updated as of 17 October 2008. They give the specs for the universe in two versions: based on WMAP alone and based on ALL the data, what they call "WMAP+BAO+SN" (microwave background + galaxy counts + supernovae).
When you read their tables make sure you read the column based on all the data, labeled
WMAP+BAO+SN

What you might want is Table 2 on page 4.
Either the volume of the universe is infinite, or it is finite and in the finite (positive curved) case they give a lower bound on the size.
In that case space would be a hypersphere with radius of curvature R_curv which is currently AT LEAST 100 billion LY.

They use a convenience number of h = 0.71 in their tables which allows the figures freedom to change if the Hubble rate is revised (it is currently estimated around 71 km/s per Mpc). That is a technicality, just remember that when they put in h they mean 0.71

So you look in Table 2 and it says R_curv > 22/h Gpc.
22/0.71 = 31
a parsec is 3.26 lightyears.
so that means 31 x 3.26 billion lightyears.
It comes to 101 billion but let's round it to 100 billion.
That is our basic handle on the size of the universe. If it is finite then the simplest guess is that space is the 3d analog of the 2d surface of a balloon, a hypersphere. And the radius of the hypersphere is at least 100 billion LY. If it is not finite, well, then it is infinite

There are some exotic finite volume cases one might also consider. Toroidal. Donut shapes, etc. They don't consider those here. I'd rather neglect them too.

The volume of a hypersphere with radius R is 2pi² R³
2pi² is approximately 20. So you can figure the volume in cubic lightyears, or cubic meters, if you like.

This is a lower bound. It could be infinite. Data are getting better on whether it is finite (the positive curvature case) or not. We may know in a few years.
==========================

One way to get that figure of 45 biilion ly is to google "wright calculator"
and actually use Ned Wright's calculator to find the current distance to the matter which emitted the background radiation we are now receiving.
The redshift of the CMB radiation is 1090.

So you just type in 1090 for z (the redshift) and it will tell you that the source matter is now 45 billion LY away from us.

It will also tell you how close it was to our matter (that became Milkyway) when it emitted the light---that is what is listed as "angular size distance", so put in z = 1090 and read off angular size distance. It should come to 41 or 42 million LY.

The distance from us to them has stretched out about 1090-fold in the time the light has been traveling and also the wavelengths of the light have been stretched out by the same factor, about 1090-fold. That stretching, of both distances and wavelengths, took about 13.7 billion years and during that time the CMB light has been on its way to us.

Anyway, if you want, specify what would be good to put in your paper and anyone around can contribute. I didn't see your post earlier because it was not in Cosmo forum. Sorry.

 

[Denton]

Sorry, I don't understand how 'space' can expand faster than the speed of light. If particles are moving away from each other at say 51% c, doesn't special relativity say that velocity addition doesn't apply there? As in relative to each other the other one is not moving at 102% C.

 

[cristo]

Sorry, I don't understand how 'space' can expand faster than the speed of light. If particles are moving away from each other at say 51% c, doesn't special relativity say that velocity addition doesn't apply there? As in relative to each other the other one is not moving at 102% C.

The important point to realize is that galaxies are not moving through space, but that the distances between galaxies are increasing faster than the speed of light because space is expanding. A standard way to think about this is using the so called 'balloon analogy.' Take a partially inflated balloon and mark several dots on it, then blow the balloon up. The surface of the balloon is an analogy of the universe, and the dots are galaxies. Now, in blowing the balloon up, you will notice that the distances between galaxies increase, but the galaxies are not moving through space. It is this increasing distance (colloquially called the expansion of space) that gives rise to the faster than light speeds.

I hope that helps: maybe someone else will come along with a better explanation. The take home message, though, is that instead of thinking of the expansion of space as some physical process, simply think of it as a shorthand for 'distance scales are increasing.'

 

[Chalnoth]

The really short answer is, "we don't know," while the somewhat more detailed answer is, "What do you mean by 'size'?"

The primary issue here is that there is a limit to how far we can see, a limit set by the emission of the cosmic microwave background. And at the edge of what we can see, the universe is almost completely uniform, which indicates that it must go on much further than what we can see. So we can't say just how big the entirety of our universe is, and we certainly can't say how many times events that start of regions like our own have occurred or will occur (it might be one or infinity or anywhere in between).

So, if we instead step back and start talking about sizes that we can actually measure, such as the distance to the cosmic microwave background, we can get an idea as to the size of the region of the universe which we can observe. Others have posted good descriptions as to how that is done.

 

[Chalnoth]

Sorry, I don't understand how 'space' can expand faster than the speed of light. If particles are moving away from each other at say 51% c, doesn't special relativity say that velocity addition doesn't apply there? As in relative to each other the other one is not moving at 102% C.

Ah, well, this is just because the expansion of the universe isn't measured in units of speed. How can you apply a speed of light limitation to something with units of inverse time?

And as far as objects in the universe are concerned, speed is only well-defined locally. In General Relativity, it only makes sense to compare speeds of objects at the same point in space-time, so if you want to talk about something's speed and how it compares to that of light, you have to compare it against light rays moving right next to it.

This fact gives rise to the idea of horizons: in some regions of the universe, light rays emitted can never reach certain other regions of the universe. A somewhat more familiar example of this is a black hole, where inside the event horizon an outgoing light ray actually travels inward to the center of the black hole. This is why nothing can escape a black hole: it'd have to outrun a light ray.

A similar thing happens in a universe dominated by dark energy: light rays from far away objects can never reach destinations that are too far away because by the time it has traveled a part of that distance, the distance between the light ray and the destination has increased by a greater amount. If there were no dark energy, or if the dark energy eventually dwindled away to nothing for some reason, and the universe were flat or closed, eventually the expansion would slow down enough that the light ray could reach the far-away destination.

 

[Rocketjj]

Whoa, thanks for all the help guys, my brain is fried after all that!

It seems the actual size of the universe (rather than observable) is too complicated for what I want to write (very Interesting, however).

May someone maybe clarify if what I say here is correct?

'The observable universe is the region of space in which we can theoretically observe. Light takes billions of light years to reach us, so we can not yet theoretically see things beyond the edge of the 'observable' universe. One would assume that for every year of earth, we could see a light year further so to speak. However, light hitting us from 14billion light years away will be from a star which is now ~47billion LYs away due to the expansion of the universe.'

Thanks again for the replies guys, very helpful :)

 

[mgb_phys]

It seems the actual size of the universe (rather than observable) is too complicated for what I want to write (very Interesting, however).

Pretty much - even then there are different philosophies in cosmology.
From pure observationalists that say anything outside the observable universe is not-observable and so isn't physics - it might well exist but since we can't measure it then it's maths or philosophy. To other more open minded astronomers that believe in many universes.

'The observable universe is the region of space in which we can theoretically observe. Light takes billions of light years to reach us, so we can not yet theoretically see things beyond the edge of the 'observable' universe.

I would be ok with that

One would assume that for every year of earth, we could see a light year further so to speak.

Not quite, the observable universe doesn't expand at 1lyr/yr - remember the universe is still expanding, although not as fast as it was in the beginning

However, light hitting us from 14billion light years away will be from a star which is now ~47billion LYs away due to the expansion of the universe.'

And was only 500,000 lyr away when the light was emitted - to split hairs we don't see 'stars' that far back - you would be better saying object, we can only see very bright early objects like quasars

 

[Rocketjj]

And was only 500,000 lyr away when the light was emitted - to split hairs we don't see 'stars' that far back - you would be better saying object, we can only see very bright early objects like quasars

Ah yes of course, objects would definitely be a better term. Thanks very much.

edit - I am not sure I follow on the 500,000 light year part. Do you mean that the source of the light was at one point 500,000 lyr away, by the time this light reached earth, it appeared that it was 14blyr away due to expansion of the universe. Meanwhile the source of the light is now actually 47 blyr away?

 

[Chalnoth]

edit - I am not sure I follow on the 500,000 light year part. Do you mean that the source of the light was at one point 500,000 lyr away, by the time this light reached earth, it appeared that it was 14blyr away due to expansion of the universe. Meanwhile the source of the light is now actually 47 blyr away?

Well, not quite. The way that the time part works is by using comoving clocks.

The idea with a comoving clock is that you imagine a clock that starts in the area that eventually becomes where we are, as well as one that starts in the area that eventually becomes the part of the universe we're looking at. These clocks are originally synchronized so that they show the same time when they observe that the universe around them is the same temperature. Then the clocks just sit there and tick away.

Once we have an idea of a comoving clock, we can then talk about some sort of "global time". First we usually set t=0 to be the time when, according to the classical big bang theory the universe was in a singularity (this time never existed, by the way: something else had to happen before the universe was so dense, but it's a convenient point to set t=0). If we set t=0 to be that time, then the CMB is emitted when all comoving clocks read a few hundred thousand years (I forget exactly...around 250,000 or somewhere thereabouts). At this time, things in the universe were also a little over a factor of a thousand closer together than they are now. Therefore the photons in the CMB that we see today were emitted from matter that was, at that time, somewhere around 46 million light years away. According to a comoving clock, it wasn't until some 13.7 billion years later that the light reached us, just because for every bit the light traveled, it lost ground due to the expansion of the universe. So even though it started quite close (around 46 million light years away), it took all that time to get here, and now the matter that emitted that light is around 47 billion light years away, with "now" defined by having the same time showing on our respective comoving clocks.

 

[mgb_phys]

edit - I am not sure I follow on the 500,000 light year part. Do you mean that the source of the light was at one point 500,000 lyr away, by the time this light reached earth, it appeared that it was 14blyr away due to expansion of the universe. Meanwhile the source of the light is now actually 47 blyr away?

Not quite.
note - the 500,000 light years was just an example - it doesn't mean anything.

The earliest light comes about 380,000 years after the big bang that's when the universe cooled enough for light and matter to exist separately - that's was around 14bn years ago (give or take 0.5Bn)
That light now forms the cosmic microwave background which we see everywhere and is 47bn lyr away (or so).
We (or the bit of space that would later become our us) could have been very close to that light but as the universe expanded the source of the light and us moved apart.
Note that the universe expansion doesn't violate the speed of light limit because no information can pass between expanding parts faster than light - there is no rule against space itself expanding.

There are a bunch of threads in the cosmology forum talking about this - it's always tricky to find a balance between making it understandable and not saying anything that is actually false.

 

[marcus]

edit - I am not sure I follow on the 500,000 light year part. Do you mean that the source of the light was at one point 500,000 lyr away,...

...Therefore the photons in the CMB that we see today were emitted from matter that was, at that time, somewhere around 46 million light years away. According to a comoving clock, it wasn't until some 13.7 billion years later that the light reached us, just because for every bit the light traveled, it lost ground due to the expansion of the universe. So even though it started quite close (around 46 million light years away), it took all that time to get here, and now the matter that emitted that light is around 47 billion light years away,...

Not quite.
note - the 500,000 light years was just an example - it doesn't mean anything.

The earliest light comes about 380,000 years after the big bang that's when the universe cooled enough for light and matter to exist separately - that's was around 14bn years ago (give or take 0.5Bn)
That light now forms the cosmic microwave background which we see everywhere and is 47bn lyr away (or so).
We (or the bit of space that would later become our us) could have been very close to that light but as the universe expanded the source of the light and us moved apart.
Note that the universe expansion doesn't violate the speed of light limit because no information can pass between expanding parts faster than light - there is no rule against space itself expanding.

There are a bunch of threads in the cosmology forum talking about this - it's always tricky to find a balance between making it understandable and not saying anything that is actually false.

Rocket, you are getting pretty good answers but I have two suggestions.
1. go to cosmo forum to ask questions like this, and follow-up questions along the same lines. there is plenty more you can learn.

2. get some direct experience with a handy online calculator from which numbers like you are seeing here come. Like, google "wright calculator" or go to
http://www.astro.ucla.edu/~wright/CosmoCalc.html
and put in z = 1090 the redshift of the CMB (cosmic microwave background).

Press either "flat" or "general" and the calculator will immediately tell you that the CMB light has been traveling for 13.7 billion years. And the source matter that emitted it used to be 42 million LY from our matter, back when the light was emitted.

And the source matter is now (as we are receiving the light) 46 billion LY from us.

1090 is the factor by which distances and wavelengths have been stretched out during the 13.7 billion years the light was in transit.

The calculator embodies the standard cosmological model. It is something you should know how to use. If you have questions on how to use it, or what the terminology means, please ask.

One number I would suggest you know by heart is the estimated redshift of the CMB, namely this 1090. It is the wavelength stretchout of the oldest light we can see, that used to be a reddish and infrafred mix glow, back when, and is now microwaves. Because 2 micron infrared stretched out by a factor of about a thousand is 2 millimeter microwave. Redshift symbol is z. This fact that the oldest light is z = 1090 is a basic fact about our universe. So google "wright calculator" and find the z box, and type in 1090, and see what you get. Any trouble or confusion, come back and ask.

 

[dyosa]

I believe nobody can measure it.

 

[marcus]

But it seems obvious that we do model the universe and test the model against millions of datapoints, for good fit, and estimating the size just means to derive one of several possible features of the bestfit model. We do estimate the size of the universe, among many other things about it.

Your post sounds like philosophy or mysticism. You say cannot do what we, in fact, do all the time.
You give no reason.

Maybe you should give reasons for your stated belief that we cannot estimate the size of the universe. Science is about rational belief, not irrational belief. So perhaps you should try to justify your claim that we can't estimate size.

Currently the published statements about size are of the lowerbound confidence interval type, like for example:
"With 95% confidence the presentday volume of space is at least such and such..."

Infinite volume still cannot be ruled out. But as instruments and data get better the range of estimated curvature narrows down and it is possible that infinite volume will be ruled out in the next few years, or conversely that it will be confirmed.

(To high confidence level. As a general rule in a mathematical science like this there are no certainties.)