# Diameter of the Universe

1. Jun 28, 2007

### Voltage

Can anybody tell me the accepted figure for the diameter of the universe? I rather thought it was a simple 27 billion light years, but have also picked up on the larger number of 93 billion light years due to expansion. Can you also give me some indication of how robust any estimate might be? Thanks in advance.

2. Jun 28, 2007

### CraigD

Any estimate of the diameter of the universe is going to be pretty rough. What is more concrete is the diameter of the visable universe. This then opens up a philisophical debate on the subject of what is the universe. Most models of the size of the universe are derived from the starting point of the big bang followed by equal expansion at a given rate to the point we are today. The rate is what makes the estimate rough. How you pick the rate and rate change determine the size of the universe.

CraigD, AMInstP
www.cymek.com

3. Jun 28, 2007

### chroot

Staff Emeritus
The so-called "particle horizon," the observable radius of the observable universe, is around 46 billion light-years. This is supported by WMAP data.

- Warren

4. Jul 3, 2007

### Voltage

Thanks Craig and chroot. We've moved offices, I'm sorry I've been slow getting back to you.
The leads you gave me were enough to assist me to find out what I needed to know. Maybe. Space expands so then there's more space, and that expands too, so there's an integral at work. Hence the radius is more like ½c², which in natural units where c=1, and using 13.7 billion years as the age of the universe gives a radius of 93 billion light years. We have to trim that back a little because the expansion isn't quite exponential, which means we can see a little more than half the universe. How's that sound?

Last edited: Jul 3, 2007
5. Jul 3, 2007

### marcus

You might be interested in getting a rough idea of the actual size of the universe, rather than of the chunk of it that we can see.

Those are two very different things. Warren has made it clear that he is talking about the chunk we can see (by any means, light neutrinos gravity waves whatever) and that is 46-some billion LY radius.

might be slightly more but not worth quibbling since its all rough estimates.

But you might also be interested in getting an idea of present estimates of the size of the WHOLE THING. That's a different kettle of fish. People do wonder about it though.

It could be infinite (so the diameter would not be defined).
That is actually a widely preferred view among professional cosmologists---that the big bang was infinite in spatial extent and the universe is and has always been spatial-infinite.

this is associated with the common assumption that the largescale average spatial curvature of the universe is EXACTLY ZERO. (technically they write Omega exactly = 1). A lot of working cosmologists make this assumption in analyzing data. But this practice has been questioned lately and the way they talk has changed to where they now sometimes say NEARLY FLAT meaning some slight positive curvature (translated to Omega close to one but not exactly, maybe like 1.01----the extra 0.01 is associated with the slight curvature)

This leads to a picture where space is analogous to the surface of a sphere, except it is 3D of course and the sphere surface is 2D. And so in this nearly flat, positive curved picture space HAS NO CENTER, all points in space are more or less equal. Like on the surface of a sphere.

And when you see a figure like Omega = 1.011 (as in a recent paper by Ned Wright) you can translate it into a rough estimate of the CIRCUMFERENCE if you want. I'll tell you what it works out to be if you want to know. That would be an idea of the spatial size of the actual U, not just a visible chunk.

Wright is a pretty good cosmologist BTW
here's his website
http://www.astro.ucla.edu/~wright/cosmolog.htm

http://arxiv.org/abs/astro-ph/0701584
Constraints on Dark Energy from Supernovae, Gamma Ray Bursts, Acoustic Oscillations, Nucleosynthesis and Large Scale Structure and the Hubble constant
Edward L. Wright (UCLA)

======
I should say there is also the negative curved possibility with Omega slightly less than one, like 0.99
but that has kind of dropped out of the picture in recent years and you hear less about it.
the published confidence intervals for Omega are mostly on the upside of 1, these days, like [1.00, 1.02]
so they consider the negative curve case less and less.

Last edited: Jul 3, 2007
6. Jul 4, 2007

### Voltage

Thanks marcus, I'll check it out.

Please note that I was talking about the diameter of the actual universe. By some strange quirk the radius of the whole caboodle seems to be double that of the particle horizon. Assuming perfect exponential expansion since the big bang and natural units, ½c² gives me

½ * 13.7 * 13.7 = ½ * 187.69 = 93.845.

That's the radius of the universe in billions of light years. The diameter is 187.69 billion light years but that's a maximum, because the expansion is perhaps a little less than exponential.

I found what looked like very useful information from Neil Cornish at Montana State University, interviewed by Robert Roy Britt who wrote an article Universe Measured: We're 156 Billion Light-years Wide! in 2004. See:

http://www.space.com/scienceastronomy/mystery_monday_040524.html

I also found Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the universe by Tamara M. Davis and Charles H. Lineweaver at the University of New South Wales in Sydney. It dates from 2003, and what’s particularly interesting is all the examples of misconception starting on page 21.

http://arxiv.org/abs/astro-ph/0310808

Does all this sound reasonable?

7. Jul 6, 2007

### marcus

the Davis Lineweaver is a very good article. Lineweaver is world-class.
those two also did a SciAm piece called Misconceptions about the Big Bang (or some such title) back in early 2005 that is available online.

About Cornish and Spergel, they are also highly reputable world-class cosmologists. What they were finding in the work that the reporter discussed with them was a MINIMUM size of the universe.
it could be average flat and infinite, it could be nearly flat and finite but still very big----nobody knows how big. but you can make some measurments and say that it is AT LEAST this big (otherwise we would be seeing repeat patterns and stuff which we dont see)
=================

So your question to me is, is your research, what you are digging up REASONABLE. I say yes it is very reasonable. My view is that it is far more important to be asking yourself questions and digging for answers---especially if you are coming up with legitimate top-grade stuff like from excellent mainstream people. It is more important to do what you are doing than that you should be having all the correct thoughts by somebody else's standards and saying the correct things by their standards...

I have my own ideas about the size of the universe but I will not lay them on you as a dogma. Keep doing independent research!

8. Jul 6, 2007

### marcus

Better learn to use the arxiv search tool if you dont already

http://arxiv.org
click on "search"
get http://arxiv.org/multi?group=grp_physics&/find=Search

or just go here:
http://arxiv.org/search

Put in Lineweaver for author and find all his articles, see what kind of research he does

Put in Spergel do the same

change "title" box to a second "author" box and put in a second author, like Cornish and get all the articles by Spergel and Cornish

or you can use just one "author" line and the boolean term AND
so you type in
Spergel AND Cornish

and you can type in keywords which you want to occur in the abstract (the short summary)

some people say the arxiv.org search tool is dinky, or even dorky
and it is definitely your basic, low-maintenance tool
but the database---the preprint archives--is an incredible treasure
so I find it worth its weight in googles

Last edited: Jul 6, 2007
9. Jul 9, 2007

### Voltage

Thanks very much, Marcus. I appreciate it. I'll look out for that misconceptions piece in SciAm. As regards "independent research", I'm a layman, I can't meet the expected standard and tend to be dismissed. Hence I've been keeping a low profile. But nevermind. I'd like to hear your thoughts on the size of the universe. Please do give them.

10. Jul 10, 2007

### marcus

I thank you in turn for your interest, Voltage. Many people adopt an attitude of self-restraint---since we don't know the size or even whether it is infinite or finite, they decline to speculate and will not venture a guess. (To do so would be bad scientific form.)

for a lark, I will break the normal etiquette and tell you that I think it could well be spatial finite, topologically equal to S3, with overall positive curvature corresponding to a radius of curvature of 130 billion lightyears.

If you want, I can calculate the volume in cubic lightyears
that would be the volume at the present moment, since it is increasing.

there is a standard estimate of the matter density, which I accept as right and which in energy terms comes to about 0.8 joules per cubic kilometer.

If you want I could convert that to joules per cubic lightyear
and multiply by the volume to get a rough estimate the total energy content, at the present moment.

All that would be based on a January 2007 paper of Ned Wright where he gave a "best fit" estimate of Omegatotal = 1.011.
If you actually BELIEVE that, everything else follows from that plus the usual figure for the Hubble constant.
http://arxiv.org/abs/astro-ph/0701584

According to serious science etiquette, however, you are not supposed to take that best-fit estimate seriously because there is still a bunch of uncertainty, and possible other models besides the LCDM that his estimate is based on assuming.

So what I'm demonstrating here is more a kind of play activity. I wouldn't get up at an astronomy conference and declare that the universe radius of curvature was 130 billion lightyear

But I still might quietly remind people of the Omegatotal = 1.011 estimate and let them draw their own conclusions.

Last edited: Jul 11, 2007
11. Jul 11, 2007

### marcus

Voltage, I worked the volume out, in case you or anyone was interested.

The presentday space volume of Ned Wright's "best fit" LCDM universe is

4.4 E 34 cubic lightyears.

or if you like this notation better

4.4 x 1034

==================
don't blame Ned Wright if you don't like this result. All he contributed was he took the standard LambdaCDM model----the thing with a cosmological constant Lambda in it-----and he fitted it to four or five different sets of data, the best and latest available. And he got a "best fit" estimate of
Omegatotal = 1.011.
http://arxiv.org/abs/astro-ph/0701584

the rest I derived from that, using some notes by George Smoot.
I take responsibility for any arithmetic errors. Anybody want to check my work? Questions?
===================

Here is some extra stuff, not necessarily for Voltage or anyone in particular. If you want to calculate the volume of S3 remember that it is the 3D "surface" of a 4D ball.
the 3D volume of that "surface" is $$2\pi^2R^3$$

So to get the volume we have to plug R = 130 billion LY into this
$$2\pi^2R^3$$

As everybody probably knows, pi-square is about 10 and so
$$2\pi^2$$ is 20
and the cube of 1.3 is 2.2, so if R is 130 billion LY then
$$R^3$$ is 2.2 E33 cubic LY
Therefore, multiplying by 20, the volume of all space at the present moment is
4.4 E34 cubic LY.

Last edited: Jul 11, 2007
12. Jul 11, 2007

### Voltage

Thanks for all that Marcus.

I've printed the paper and skimmed it, and will read it properly offline. I have to say I'm surprised about the large size and the omega > 1. That doesn't fit at all with the mental picture I've been forming. To tell the truth, lambda cold dark matter doesn't much fit with my mental picture either, but that's why I'm here. To find out things and get a better mental picture.

Thanks again. Must study.

13. Jul 11, 2007

### marcus

just for fun I calculated the mass of the matter in the "best fit" LCDM universe using the currently preferred values of parameters, like 71 for the Hubble and 27 percent as the matter fraction (ordinary + dark)

I left out dark energy (the 73 percent) because I just wanted the answer in metric tonnes of matter.

the mass of matter in a cubic lightyear works out to 2.55 E18 tonnes.

So we just have to multiply that by the number of cubic lightyears which is 4.4 E34 in the "best fit" LCDM.

It comes to 1.1 E53 tonnes of matter in the whole universe, at present. Hopefully that stays about constant, can't think why it should change.

14. Jul 12, 2007

### Voltage

Marcus: Is that just matter, or are you including energy?

Wow, there sure are a lot of out of date web pages on this sort of thing, it's hard to know what to trust. This one looked interesting though:

http://www.astro.ucla.edu/~wright/neutrinos.html

It says there's circa 337 neutrinos and circa 441 CMB photons per cubic centimetre of space. That's a lot of energy, quite a big mass equivalent.

Let me just look at that number:

110,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 tonnes.

Sure is big. Ain't physics fun?

Last edited: Jul 12, 2007
15. Jul 12, 2007

### marcus

I'm including neutrinos and photons with the matter. The only thing left out is dark energy---the enigmatic 73 percent

Thanks for that link! I don't recall ever happening to surf that one. I've relied on Ned Wright's webpages a lot, and don't recall ever finding a mistake. (I'm a non-specialist cosmology-watcher, not a cosmologist, so I'm not really set up to judge----but I think of him as a pretty good authority)

Even though there are a huge number of CMB photons, they don't amount to a major fraction of the mass-energy, compared with gas, dust, stars etc. The energy of each photon is so small. I remember seeing a detailed INVENTORY of all kinds of stuff including neutrinos and starlight and CMB etc along with types of ordinary matter. Even though the photons are so plentiful they didnt amount to even 1 percent.

curiously even though CMB photons dont represent a big slice of the ENERGY equivalent inventory they represent the overwhelming majority of the ENTROPY in the universe. You could get somebody (Wallace, Pervect, Russ Waters etc.) to explain this I guess. When you estimate the entropy you can essentially throw out all the other sources and just compute it for the CMB and that is good enough for government work.

this is IIRC, get somebody else to confirm before you believe it
Absolutely

16. Jul 13, 2007

### Voltage

Thanks again marcus. Much appreciated.

17. Jul 18, 2007

How can the universe have a defenite diameter if it is constantly expanding?

Probably me being stupid again.

18. Jul 18, 2007

### Voltage

Well, it doesn't, but when we're talking of a figure like 188 billion light years, what's a few light years between friends?

19. Jul 18, 2007

### marcus

We were talking about the PRESENT DAY size of the universe.
yes it is expanding but distances take approximately 140 million years to expand one percent. So the size doesnt change all that fast.

It is a little confusing for you to ask about the DIAMETER since in the "best fit" LCDM universe space is not a ball

It is more like the surface of a 4D ball---a kind of 3D sphere.
I could tell you the CIRCUMFERENCE---the length of a great circle

but talking about a radius or diameter would take us out of the space we are living in, conceptually it is not related to the volume in the usual way we're familiar with

think about the surface of a balloon where the analog of volume is area, from the standpoint of a flat being who lives in that surface. there are problems for him of what the radius or diameter means because he doesnt see any space outside his own world. he may know the AREA (like we might know the total volume) but the idea of radius might not make sense for him.

If you are all right with a distance in 4D space, then the radius of curvature of the "best fit" LCDM model is 130 billion LY
and the circumference would be 2 pi times that
which is 817 billion LY.

if you could travel 817 billion times the speed of light, in a straight line, then if you set off in a certain direction you would come back to the same spot (relative to the cosmic microwave background) a year later
because distances expand so slowly, a year makes hardly any difference. the circumference next year would still be essentially what it is today----but traveling at light speed, a round trip tour would take so long that distances would have gone way expanded, so it is not a practical thing to envisage doing.

Last edited: Jul 18, 2007
20. Jul 19, 2007

### chrisina

1.Distance TODAY between us and the furthest observable star: 46 bill. LY
(will increase in the future)

2.Distance TODAY between us and the furthest star in the universe: unknown but for sure much bigger than 1., maybe infinite ?
Not enough precision on the measurement of Omega to make a precise statement.

3.Distance TODAY between us and the furthest star that will ever receive a signal emmitted today from us : 16 bill. LY
(will decrease in the future !)

Basis : LamdaCDM Omega M = 0,3 , Omega Lambda = 0,7, H0 = 70 s-1

21. Jul 20, 2007

### Voltage

You know marcus, I don't buy that.

22. Jul 20, 2007

### marcus

I don't have any need to convince you

I am just giving you elementary geometric characteristics of the "best fit" version of the LCDM.

You don't have to believe in the LCDM model universe, nobody does. It is just the mainstream consensus model that working cosmologists use. So its good to know about whether you believe it or not.

LCDM comes mainly in two flavors. Flat infinite Omega = 1 exactly.
and the other that you tend to hear about is like Wright's "best fit" LCDM which is around Omega = 1.01
He actually says 1.011.

So if you put that together with the accepted value of Hubble parameter which is 71, then you get that space is a 3-sphere with radius of curvature 130 billion LY. (a radius of curvature is not a real radius that you could travel along--it is the analog of the radius of the balloon for a 2D being who lives in the 2D surface of the balloon)

the analog to picture a 3-spehre, is a 2-sphere which is the surface of a balloon.
a 3-sphere is the skin of a 4D ball. the radius of curvature is the radius of that 4D ball
and the experience of living in a 3-sphere is almost indistinguishable from living in infinite flat 3D space----locally it feels just the same

the radius of curvature is so big that the geometry is virtually flat.

3-sphere is a way to reconcile the ideas of boundaryless, finite, and yet locally flat.

I think it is a really nice geometry, partly because it is finite and has no boundary, partly because it is the simplest possible.

I don't see why you don't buy it, Voltage, but you shouldn't feel obliged to explain. to me it is a no-brainer---the obvious choice you think of if you want to picture an alternative to the INFINITE flat space version of LCDM.

23. Jul 20, 2007

### chrisina

The problem, Marcus, is that as we get closer to 1 on the measurement of Omega, a very small % error makes the estimate on the radius of the Total universe increase by a huge amount.

So I think its best to focus on lambda CDM model with omega = 1 (0,3+0,7), and the two radiuses that have relevance and can be estimated with a sufficient degree of precision (+/- 10% with current data) :

- the radius of the observable universe : 46 bill LY today (to answer madphysisict, you are right, because of expansion, this value is only valid now, and not in a few billion years, when it will be bigger.)

. the radius of the "reachable universe" (event horizon) : 16 bill LY today
This is the key diameter we have to focus on as far as future space exploration goes, as even if one day we are able to travel at the speed of light by sending the corresponding information (very hypothetical, but why not), it will never be able to reach stars which are beyond that reach, even in an infinite amount of time.

The tricky thing to understand is that because of the accelerated expansion of the universe the "reachable" universe as a proportion of the "observable" universe will decrease. In other words, will still be able to see all the same galaxies (pictures of them in the past), but as far as reaching them (in the future), we'll be able to reach less and less.

24. Jul 20, 2007

### marcus

Chrisina, the trouble with what you say is that it is off topic. The original poster, Voltage, was not talking about the size of the observable universe, or about the particle horizon. Voltage already knew about the particle horizon and was explicitly asking about the size of the WHOLE THING.

Voltage quoted research by Neil Cornish, which again was about getting a lower bound for the present spatial size of the WHOLE universe.

My general principle is that we should try not to confuse people by CHANGING WHAT WE ARE TALKING ABOUT in the middle of a thread. So I feel your trying to divert attention to things like the particle horizon and the size of the observable is counterproductive.

Last edited: Jul 20, 2007
25. Jul 20, 2007

### marcus

Chrisina, near the start of the thread I mentioned the particle horizon and also could well have but didn't mention the event horizon, also a very interesting distance as you point out. A I ASKED Voltage did he mean horizons stuff or did he mean the size of the WHOLE.
And it seems that he replied clearly that it was the whole thing. No offense, but the size of the whole is something that rarely gets discussed so I welcome the opportunity and think we should stick to that.