What is the accepted diameter of the universe?

[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.

 

[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

 

[chroot]

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

 

[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?

 

[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

here's his recent paper (click on the PDF to download)
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.

 

[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?

 

[marcus]

...

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?

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 don't 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!

 

[marcus]

Better learn to use the arxiv search tool if you don't 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 Cornishor 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

 

[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.

 

[marcus]

Thanks very much, Marcus. I appreciate it. I'll look out for that misconceptions piece in SciAm. ... But nevermind. I'd like to hear your thoughts on the size of the universe. Please do give them.

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 Omega_total = 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/0701584According 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 Omega_total = 1.011 estimate and let them draw their own conclusions.

 

[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
Omega_total = 1.011.
http://arxiv.org/abs/astro-ph/0701584the 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.

 

[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.

 

[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.

 

[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?

 

[marcus]

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

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

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.

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 don't 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

Ain't physics fun?

Absolutely

 

[Voltage]

Thanks again marcus. Much appreciated.

 

[madphysics]

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

Probably me being stupid again.

 

[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?

 

[marcus]

Madphysics,
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 doesn't change all that fast.

...

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
Omega_total = 1.011.
http://arxiv.org/abs/astro-ph/0701584the rest I derived from that, ...

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 doesn't 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.

 

[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

 

[Voltage]

..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..

You know marcus, I don't buy that.

 

[marcus]

You know marcus, I don't buy that.

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.

 

[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.

 

[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.

...
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...

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.

 

[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.

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).
...

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.

Chrisina, you may have a predetermined idea of what we OUGHT to be asking about. You may think we ought NOT to ask about the size of the universe (perhaps because it is very hard to discover) and that we ought to be asking about the very interesting distances like the event horizon (around 16 billion LY) and particle horizon (40-some billion) perhaps because we can estimate these things and say reasonable stuff about them. But these are radically different ideas of size---they measure different things. Since it can get confusing if one says "size of universe" and means different things, I suggest that you START A THREAD about the event horizon, which you call the radius of the "reachable universe" for someone going the speed of light.

the present distance away of things that could today send a flash of light that would reach us, is another way to think of it.

That could be an interesting thread and you could discuss the cosmological event horizon and how it depends on Lambda etc.

But let's keep this thread to be about Voltage original question, which is about the size of the whole thing.

 

[Voltage]

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.

I do feel obliged to explain, marcus. But I can't present the model with enough rigour to avoid being in breach of forum guidelines. Perhaps at a later date.

 

[marcus]

I do feel obliged to explain, marcus. But I can't present the model with enough rigour to avoid being in breach of forum guidelines. Perhaps at a later date.

Well, I admit what you say makes me curious to know. If it only takes a few words, you could send me a PM (private message).

It seemed to me earlier that you were arguing for an upperbound on the size (it can't be any larger than such and so)
by starting with an idea of the size at the start of expansion
and by assuming some kind of bound on the SPEED of expansion.

that seems like a physical-type argument (it doesn't get off into philosophy or metaphysics). I think that I could counter that argument within the context of mainstream consensus cosmology, which is the rules I try to play by, plus a little quantum cosmology where the mainstream model doesn't have anything clear to say.

If that is how you argue, then I'm interested but I don't think your argument has a prayer of being right.

Mainstream cosmology, whatever's based on classic einstein GR, does not HAVE any limit on expansion speed. it can be any finite speed.

and to talk about the size (of the whole thing) at the start of expansion you have to go outside the bounds of classic 1915 einstein. as far as we know, singularities do not exist in nature, they only exist where theories break down, so its not meaningful to talk about the starting size in classic GR.

they only do that in popularization books, where they talk about the tiny size of what eventually became the observable universe, they never talk about the initial size of the whole thing because the size of a singularity is not well-defined. that's all pop sci anyway

there are quantized models where you don't have a singularity
and then you can talk about the size at the moment of BOUNCE which replaces the singularity, so you can talk about the initial size at the start of expansion but to do it you have to go outside the bounds of the classic 1915 theory, and its hard.

So I don't think you or anyone can get a grip on the size of the universe that way----mainly because there is no known bound on the speed of expansion.

I think the only way to get a handle on it is by measuring Omega, essentially measuring the large scale curvature.

But if you want, boil your argument down to a brief message that says roughly how it goes and send it PM and I will look at it. I may not be able to comment helpfully, but I'm curious, so you are welcome to do it if you want.

 

[chrisina]

Point taken Marcus, so let's talk about the size of the overall universe.

But how can we discuss this issue without having a validated theory of gravitation that works at Planck scales ?

GR, the FRW metric and the Lambda CDM model, associated with the measurements of the various omegas based on the CMBR data can enable us to make scientific projections of what our observable universe looks like and has evolved.
Should we extrapolate from there all the way to Planck densities and make projections for the overall universe assuming that this model would work all the way, that and inform us on the overall topology of the universe ?

Do you think that the answer to that question ( the size/topology of the overall universe) is going to be the same if you asked it to Bojowald and you asked it to Linde ? Will the result to that question be the same (even by orders of magnitude) if you assume that the universe evolved from a quantum bounce model based on LQG, or if you assume something completely different.

So, as frustrating as it maybe, I think "WE DON'T KNOW" is the answer to that question. Of course, that doesn't mean the question is not valid, interesting, passionating. But sometimes, we have to pause for a second, and accept that there are things that we do not know yet.

So, let's look at the following press article :
Universe Measured: We're 156 Billion Light-years Wide!
http://www.space.com/scienceastronomy/mystery_monday_040524.html

And let's look at the corresponding scientific paper by Neil Cornish :
Constraining the topology of the universe.
http://arxiv.org/PS_cache/astro-ph/pdf/0310/0310233v1.pdf

What is the key assumption in this paper ? See page 2 :
"the key assumption in this analysis is that the CMB fluctuations come primarily from the surface-of-last-scatter and are due to density and potential terms at the surface of last scatter"

Do we have an agreed upon model that generates these density and potential terms ?

 

[marcus]

...

So, let's look at the following press article :
Universe Measured: We're 156 Billion Light-years Wide!
http://www.space.com/scienceastronomy/mystery_monday_040524.html

And let's look at the corresponding scientific paper by Neil Cornish :
Constraining the topology of the universe.
http://arxiv.org/PS_cache/astro-ph/pdf/0310/0310233v1.pdf

the Cornish paper you mention came out in 2003. I recall having fun discussing it back in 2004 on several discussion boards.
Neil Cornish had posted on his website a photo of himself with his pet monkey on his shoulder.
Two of the co-authors of that paper are famous: Glenn Starkman and David Spergel. I don't know about the fourth author.

The results in that paper do not constrain what I am talking about to any significant extent-----they give a LOWER BOUND showing that the diameter of a hypothetical "hall-of-mirrors" cell is AT LEAST such and such. But the "best fit" diameter I am talking about is way much bigger.

Cornish has a more recent paper improving the 2003 results slightly, but still not directly relevant to what we are discussing here-----too weak: their lowerbound does not come close to the sizes based on radius of curvature.

But it still might be fun to discuss the Cornish paper, as you propose. Here is the abstract:
http://arxiv.org/abs/astro-ph/0310233
Constraining the Topology of the Universe
Neil J. Cornish, David N. Spergel, Glenn D. Starkman, Eiichiro Komatsu
(Submitted on 8 Oct 2003)

"The first year data from the Wilkinson Microwave Anisotropy Probe are used to place stringent constraints on the topology of the Universe. We search for pairs of circles on the sky with similar temperature patterns along each circle. We restrict the search to back-to-back circle pairs, and to nearly back-to-back circle pairs, as this covers the majority of the topologies that one might hope to detect in a nearly flat universe. We do not find any matched circles with radius greater than 25 degrees. For a wide class of models, the non-detection rules out the possibility that we live in a universe with topology scale smaller than 24 Gpc."

I would urge relying directly on the paper, and not referring to the SPACE.COM popularization because I think the reporter's paraphrase introduces some confusion. As usual, to find out what they actually said you have to look at the journal article.
I don't think the "key assumption" you quote is controversial, however. Here is another quote:

==quote from Cornish et al==

The WMAP data suggest that the Universe is very
nearly spatially flat, with a density parameter
Omega = 1.02 ± 0.02[4]. Our universe is either Euclidean, or its
radius of curvature is large compared to radius of the
surface of last scatter. For topology to be observable
using our matched circle technique we require that the
distance to our nearest copy is less than the diameter
of the surface of last scatter, which in turn implies that,
near our location and in at least one direction, the funda-
mental cell is small compared to the radius of curvature.
Given the observational constraint on the curvature ra-
dius, it is highly unlikely that there are any hyperbolic
topologies small enough to be detectable [9], and there
are strong constraints on the types of spherical topologies
that might be detected [10]. Naturally, the near flatness
of the Universe does not place any restrictions on the
observability of the Euclidean topologies. Remarkably,
the largest matching circles in most of the topologies we
might hope to detect will be back-to-back on the sky
or nearly so.
==endquote==

You can get an idea from this what their conceptual map looks like. The essential yardstick they are using is the RADIUS OF CURVATURE which is either infinite (in the euclidean flat LCDM case) or some very large distance like the "best fit" estimate 130 billion LY I mentioned earlier.

There analysis does not get a grip on the radius of curvature---rather it concerns the possibility of a "hall-of-mirrors" effect of some complicated topology in which there is a FUNDAMENTAL CELL of a size which is substantially smaller than the radius of curvature.
They are trying to RULE OUT a hall-of-mirrors situation by saying "well we can't rule it out absolutely, but if there is some fundamental cell then it has to be at least this big, because if it were any smaller than that we would have seen repeating patterns in the CMB".

The distance they estimate is at least 78 billion LY (see where the abstract says 24 Gigaparsecs) is a DIAMETER OF THE FUNDAMENTAL CELL, in some repeating pattern assuming one existed, or another way to picture it is that in a hall of mirrors you see COPIES OF THE OBSERVER which is yourself and there is an apparent distance between copies which corresponds to the size of the repeating cell.

 

[marcus]

Just want to repeat what I said in post #5

...
It could be infinite (so the diameter would not be defined).

We have no certain knowledge of the size of the universe, and in fact the size might not even be defined (because it might be infinite).

The LCDM model (that cosmologists normally use and that fits the data remarkably well) might be wrong too.

But we can say certain things ASSUMING that the LCDM model is right. If you assume the LCDM picture then the best fit to data currently available is with Omega = 1.011.

Essentially that means space is a 3-sphere with circumference 400 billion LY.

Anyway that is the simplest picture of something giving Omega = 1.011.
Cornish and friends have tried to rule out more complicated ways it could happen. Like maybe what I said (3-sphere with 400 billion LY circumference) is just a hallofmirrors ILLUSION created by a much smaller universe with complicated TOPOLOGY. It is a repugnant thought, but you have to consider such possibilities, annd Cornish et al tried to rule them out as well as they could.

So although we don't know the size of the universe (and it might be infinite and not even have a definite size) we DO KNOW certain things based on reasonable assumptions of the sort usually made, and in particular we know that

if you take the best fit to today's data using the currently favored (LCDM) model then, excluding more complicated topology, you get space looking like a 3-sphere with 400 Gly circumference.)

And if you want, think of the 3-sphere as bumpy and puckery with the local curvature created by clusters of galaxy, and the zits of black holes etc. All Omega tells us is the average curvature.

And think of it expanding, if you want. One percent every 140 million years or so. A huge gas-bag full of four-dimensional gas

Keeping in mind that the figure of 400 is uncertain by a factor of two at least---it is only Ned Wright's "best fit"---and could actually be infinite.

 

[Voltage]

It seemed to me earlier that you were arguing for an upperbound on the size (it can't be any larger than such and so) by starting with an idea of the size at the start of expansion and by assuming some kind of bound on the SPEED of expansion.

I suppose I was. But I didn't mean to argue, I just wanted to find out what the currently accepted figure was for the size of the universe and be able to give a "reasonable" explanation. Maybe I was being too assumptive.

Mainstream cosmology, whatever's based on classic einstein GR, does not HAVE any limit on expansion speed. It can be any finite speed and to talk about the size (of the whole thing) at the start of expansion you have to go outside the bounds of classic 1915 einstein.

I'm a big fan of Einstein. I've read up on the original GR translation plus other material. I like to think I stick closer to Einstein than other people do. But they don't always agree that I do.

as far as we know, singularities do not exist in nature, they only exist where theories break down, so its not meaningful to talk about the starting size in classic GR.

Agreed wholeheartedly. But have you ever heard of the Weinberg interpretation? I'd say it's not necessarily the whole theory that breaks down, but some aspect of it, or some interpretation. String Theory has morphed to a huge degree, why can't GR move a little and still stay as GR?

they only do that in popularization books, where they talk about the tiny size of what eventually became the observable universe, they never talk about the initial size of the whole thing because the size of a singularity is not well-defined. that's all pop sci anyway.

IMHO there are no infinities and no singularities in nature. My goal is to make science more popular. I mean that marcus.

there are quantized models where you don't have a singularity and then you can talk about the size at the moment of BOUNCE which replaces the singularity, so you can talk about the initial size at the start of expansion but to do it you have to go outside the bounds of the classic 1915 theory, and its hard.

I definitely don't buy bounce. That's no explanation at all. Going beyond the bounds of "classic 1915 theory" is what Einstein was trying to do, and I try to stick with Einstein, so I suppose that's where I'm going.

So I don't think you or anyone can get a grip on the size of the universe that way----mainly because there is no known bound on the speed of expansion.

See your earlier point, I guess I was arguing that the ½c² for 13.7 billion years gave an upper bound.

I think the only way to get a handle on it is by measuring Omega, essentially measuring the large scale curvature. But if you want, boil your argument down to a brief message that says roughly how it goes and send it PM and I will look at it. I may not be able to comment helpfully, but I'm curious, so you are welcome to do it if you want.

I need to give it some thought.

 

[marcus]

But I didn't mean to argue, I just wanted to find out what the currently accepted figure was for the size of the universe and be able to give a "reasonable" explanation.

I didn't mean arguing in a bad sense. I meant that you were giving a logical argument---a rational deduction---about the size, based on some assumptions.

that's good. we are supposed to be doing that.

But I question your assumptions. I think your chain of reasoning breaks down because if you base things on Einstein GR then you can't say how big it was when it started expanding

AND (this is more important) you can't put a limit on the speed of expansion.

Einstein does not let you put a limit on the speed with which distances increase.

I can't respond to all of your separate points, but I'm glad you are thinking about it. Towards the end of your post where you quote me

I think the only way to get a handle on it is by measuring Omega, essentially measuring the large scale curvature...

You say

I need to give it some thought.

I hope you do give more thought to using curvature to estimate size. It is the only way I've ever known any cosmologist to do it. For example that is how Cornish et al get their basic underlying distance scale--they use the radius of curvature as their benchmark.

Again, the reason you can't use a bound on expansion speed to estimate size is because Einstein does not let you.

(His 1905 theory now called "special" relativity has a speed limit on certain kinds of motion but that does not apply to expansion of distances and it only can be applied in certain limited, i.e. special, cases. Two things within the same flat or nearly flat reference frame----not widely separated. His later theory, which he called "general", trumps the earlier 1905 theory

 

[Voltage]

I think your chain of reasoning breaks down because if you base things on Einstein GR then you can't say how big it was when it started expanding.

I was thinking of something very small compared to the current size marcus, so small that I can "reasonably" consider it to be zero.

AND (this is more important) you can't put a limit on the speed of expansion. Einstein does not let you put a limit on the speed with which distances increase.

I thought there was a limit that I could apply as at now. A while back you said that distances expand 1% every 140 million years. Working back from that they've expanded circa 7% in the last billion years, and 100% in the 13.7billion year age of the universe. This is why I thought ½c² seemed "reasonable" as the radius the universe. Perhaps I should have said d=x² where d is the diameter in billions of light years and x is the age of the universe in billions of years. This means the universe is 13.7 x 13.7 = 187 billion light years across now. A billion years ago it was 12.7 x 12.7 = 161 billion light years across, so it's expanded by 26 billion light years in the last billion years. Two billion years ago it was 11.7 x 11.7 = 137 billion light years across, so it expanded 24 billion light years in that billion year period.

The mental picture I've got is that of a universe that's akin to the "ball of gas" you mentioned earlier. It's more like a sphere of light that moves outwards in all directions at the speed of light, and also swells because there's no bag to hold it back. This is the only energy that exists. Whilst some of it is tied up as matter, there is no "outside" to the sphere, because beyond it, no energy means no gravity means no space. It's flat, it's open, it's a runaway, but it isn't a 4-sphere, there's no radius of curvature to bring you back on yourself, and it isn't infinite.

But sheesh, reading up on that conformal gravity reminded me just what a total layman amateur I am. I'd be grateful if you could put me straight on all this. Thanks for all the time you've put in so far. Meanwhile I'll read up on that radius of curvature.

 

[marcus]

I was thinking of something very small compared to the current size marcus, so small that I can "reasonably" consider it to be zero.

that is fair enough. I apologize for quibbling.

But that percentage rate only applies to the present. In the past the percentage increase per unit of time was much larger.

Maybe I should have said that distances are currently expanding at a rate of 1/10% every 14 million years.

I thought there was a limit that I could apply as at now. A while back you said that distances expand 1% every 140 million years. Working back from that they've expanded circa 7% in the last billion years, and 100% in the 13.7billion year age of the universe. This is why I thought ½c² seemed "reasonable" as the radius the universe.

Alas, I have misled you! I have not made things clear enough and you have gotten a mistaken idea. sincere apologies

You must have heard of people seeing quasars at redshift z = 7.
that means that the universe has expanded EIGHT-FOLD since the light left them on its way to us. You always add one to the redshift to get the ratio by which the universe has expanded.

You probably have heard that the redshift of the CMB is about 1100. that means that the universe has expanded about 1100-fold during the time that light has been traveling towards us from whatever emitted it (when the universe was an estimated 380,000 years old). To be pedantic one could say by a factor of 1101, but the figure 1100 is only accurate to two decimals.

I want to try to help you understand and I see you trying to estimate z-factors for various times in the past. There is an online CALCULATOR for that. this will give you an accurate figure for how much the universe has expanded in the last 1 billion years, or in the last 2 billion years

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

Your rough-and-ready calculation is a good try but the expansion history is a little more complicated and these online cosmology calculators really come in handy.

Put in 1.0 over on the left where it says "light travel time in Gyr" and press "general" (dont change the default settings)
You should get z = 0.077 over at the right. That means the universe has expanded by a ratio of 1.077 in the past billion years.
or grown by 7.7 percent. about what you estimated!

Now put in 2.0 billion years and you should get a 16.2% expansion----the ratio is 1.162.

Keep on going. You can compare it with your rough and ready estimates here:

Perhaps I should have said d=x² where d is the diameter in billions of light years and x is the age of the universe in billions of years. This means the universe is 13.7 x 13.7 = 187 billion light years across now. A billion years ago it was 12.7 x 12.7 = 161 billion light years across, so it's expanded by 26 billion light years in the last billion years. Two billion years ago it was 11.7 x 11.7 = 137 billion light years across, so it expanded 24 billion light years in that billion year period.

If you put in 10.0 billion years you should get that the expansion during that time has been by a factor of 2.815

In the past 13.0 billion years the expansion has been by a factor of 8.872

The calculator is set to arbitrarily cut off when it gets to BILLION-FOLD expansion. AFAIK You cannot make it give you a z bigger than a billion minus one.
It is really not meant to take up that close to the beginning of expansion.

=====================
ACCORDING TO MY MENTAL PICTURE best on Wright's 'best fit', at the present moment the radius of curvature is 130 billion LY. So if I use Wright's calculator and go back 13.666 billion years, that means the radius of curvature was 130 light years.

If I trust the accuracy of his calculator back to such early days, then that would be my best estimate of the size of the universe at 13.666 billion years before present.

Apart from looking at curvature, that is looking at astronomers measure of Omega, I don't think there is any other way to get a grip on the size.

But sheesh, reading up on that conformal gravity reminded me just what a total layman amateur I am. I'd be grateful if you could put me straight on all this. Thanks for all the time you've put in so far. Meanwhile I'll read up on that radius of curvature.

You are very gracious! I enjoy talking about this stuff. We all just do the best we can and I'm no great expert either. I can tell you are still picturing a surrounding space for the universe to expand into.
that isn't part of orthodox cosmology---but we can get to that another time
have fun

 

[Voltage]

Thanks for all this marcus. I'll have fun with that calculator.

..I can tell you are still picturing a surrounding space for the universe to expand into. That isn't part of orthodox cosmology...

Not at all. My picture is a whole lot less orthodox than that!

:)