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**Universe Infinite !!!**

I've heard many times that the volume or size of the universe is infinite!

But, I don't know how they say it? Is there any mathematical proof???

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I've heard many times that the volume or size of the universe is infinite!

But, I don't know how they say it? Is there any mathematical proof???

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mathman

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marcus

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It is not surprising that you have heard that the universe is infinite in spatial extent, since (although it's not known for certain) this is often taken for granted by cosmologists as a working assumption.Originally posted by Moni

I've heard many times that the volume or size of the universe is infinite!

But, I don't know how they say it? Is there any mathematical proof???

There is no mathematical proof that the universe is finite. Though it certainly might be! Neither case (finite/infinite) can be ruled out.

A good idea is to look directly at professional journal articles by prominent cosmologists and see what they say about it based on the latest observations from the Wilkinson Microwave Anisotropy Probe (WMAP).

Charles Bennet et al.

http://arxiv.org/astro-ph/0302207 [Broken]

see table 3 on page 33---"Best" Cosmological Parameters

from the article

"First Year WMAP Observations, Preliminary Maps and Basic Results"

Charles Lineweaver

http://arxiv.org/astro-ph/0305179 [Broken]

"Inflation and the Cosmic Microwave Background"

Michael Turner

"Making Sense of the New Cosmology"

http://arxiv.org/astro-ph/0202008 [Broken]

Wendy Freedman and Michael Turner

"Measuring and Understanding the Universe"

http://arxiv.org/astro-ph/astro-ph/0308418 [Broken]

The whole issue turns on how accurately they can measure a number called Omega. This is the first thing listed at the top of

Bennett's Table 3.

The current WMAP data say that Omega = 1.02 +/- 0.2

which is tantalizingly close to one.

If Omega is exactly one, then space is flat and infinite.

However, if Omega is even slightly greater than one, then space may LOOK flat but on a very very very large scale (way greater than 14 billion LY) it may curve around on itself (analogous to a sphere surface) and be finite.

Michael Turner, who is a world-renowned theoretical cosmologist, just goes right out and says "the universe is spatially flat" which is to say infinite. That is the way a lot of them think of it, because Omega has been measured so close to one. And there are some side reasons saying on theoretical grounds it ought to be flat and infinite. But based on observations, as of right now, WE CANNOT BE SURE it is infinite.

So observational cosmologists like Bennett, who heads the WMAP team, along with Ned Wright and along with Lineweaver who was a leader in the earlier COBE satellite observations, tend to be more careful and guarded----they give you a figure with error-bounds, like

1.02 plus or minus 0.02.

It could go either way.

Is Chittagong in Bangladesh?

The WMAP satellite that is currently gathering data from the Microwave Background about the shape and extent of the universe is

not even going around the earth.

They put it a million miles further out from the sun. In its own orbit around the sun. Apparently it can work better out by itself than it can if it is close in to the earth.

You see there is a lot riding on how accurate the Background can be measured! It would be great if in another year or two they could refine the figure for Omega some more and get better accuracy.

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marcus

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We could use a Cosmology Resource sticky thread

to keep basic reference links handy like the above

articles of Bennett, Lineweaver, Turner....

Here is a link that PF-poster Nereid kindly provided about

a wide-angle deep survey of the universe called GEMS

http://skyandtelescope.com/news/article_1152_1.asp

GEMS covers a patch of sky as big as the full moon

and took thousands of images in that patch

and made a mosaic picture of that patch which is

real deep, going way back in time, so you see

galaxies forming and colliding and evolving.

The article Nereid links to tells about it

and shows a portion of the picture. The total GEMS

picture has 3 billion pixels, the article says.

------------------------

Dark matter:

Here's another Nereid link to a dark matter article (mapping it in a cluster by observing lensing)

http://www.esa.int/export/esaCP/SEME3PXO4HD_FeatureWeek_0.html

------------------------

Neutrino astronomy:

Has a big future potential

in observational cosmology. Wolram, a PF-poster, provided these

neutrino-related links:

http://www.space.com/scienceastronomy/cosmic_neutrinos_030716.html [Broken]

this gives the AMANDA2 neutrino sky map---the obseratory down near south pole.

http://www.lns.cornell.edu/spr/2003-07/msg0052565.html

Basic facts/estimates about the cosmic neutrino background presented

by Ted Bunn, one of the moderators on Usenet sci.physics.research.

http://arxiv.org/abs/hep-ph/0307228

http://arxiv.org/abs/hep-ph/0112247

Two neutrino articles which surprised me, so I include them without

being able to properly evaluate or interpret. Maybe someone else can.

Observations purporting to have some bearing on the existence or

non-existence of extra dimensions. If this is too wacky tell me and I

will take it off this thread.

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marcus

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two good online cosmology calculators:

Ned Wright's

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

Siobahn Morgan's

http://www.earth.uni.edu/~morgan/ajjar/Cosmology/cosmos.html [Broken]

homepage for Siobahn in case you want to see who she is

http://www.earth.uni.edu/smm.html [Broken]

homepage for Ned in case you want to see who he is

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

-------

Martin Bojowald

http://arxiv.org./abs/astro-ph/0309478

"Quantum Gravity and the Big Bang"

General Relativity had a glitch and

quantizing the theory fixed the glitch so

it no longer predicts a moment of infinite

density and curvature (a type of singularity).

Evolution prior to big bang is shown in some

of the articles cited in this brief survey.

---------

Labguy, another PF poster, provided news of a

recent test of General Relativity

(which GR passed with flying colors) a

binary pulsar:

http://www.astro.ucla.edu/~wright/cosmolog.htm#04Dec03

The technical article about the binary pulsar

and the most stringent verification of GR to date is:

http://arxiv.org/astro-ph/0401086 [Broken]

----------

A great survey article about high energy cosmic ray observations

(another window for observational cosmology to look thru)

Floyd Stecker

"Cosmic Physics: the High Energy Frontier"

http://arxiv.org/astro-ph/0309027 [Broken]

----------

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marcus

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Useful constants:

One parsec = 3.857E16 meters

Newton's G = 6.6742E-11 cub.meter/sq.second kg

Best current estimate of Hubble parameter H = 71 km/s per Megaparsec

Critical energy density derived from that = 0.85 joule per cubic km.

----discussion of the constants---

If you put "best estimate" H into standard (SI) metric units it is H = 2.301E-18 per second, or 2.3 appropriately rounded off.

The reciprocal, or "Hubble time" parameter is 4.3E17 seconds (roughly the same as the age of the universe, as it happens).

Wendy Freedman led the Hubble Space Telescope "Key" Project to determine H with unprecedented accuracy and in 1998 they announced in effect that this (possibly the single most important) cosmological quantity, H, is

Except they dont say 0.43 quintillion seconds they either express the Hubble time in years (something like

So what does this mean about the density of energy in the universe?

It is good to have a rough idea of the

How full is it of matter, and other forms of energy?

Critical density (so-called "rho crit") is 0.851 joule per cubic kilometer, rounded off to 0.85 so as not to overstate the precision.

You can probably calculate this for yourself with the standard formula for it

"rho crit" = 3c

If you plug in the standard metric speed of light and the figure of

2.3E-18 per second and the figure given at the beginning for Newton's G, then you will get 0.85 joule per cubic km.

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Yes! You are correct! Chittagong is in Bangladesh :) And I am also the only PF member of Bangladesh :(Originally posted by marcus

Is Chittagong in Bangladesh?

The idea just came while discussing with my friend...

We all know from laws of thermodynamics:

We also know that universe is full of mass, particles that means energy!Energy can be transformed from one type to another

Total amount of energy in the universe is constant

And if the the universe is infinte, then,

So, the problem arised [b(]

Anyway! Thank you very much for you links! Those are huge links...it'll take at least a week for me! I'll read them one by one :)

I am very much interested in cosmology :) Thanks again :)

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marcus

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would not come back.

Don't worry about reading ALL the links. The important thing is

to find one good introduction to cosmology that works for you.

I have found the most useful is Lineweaver

"Inflation and the Cosmic Microwave Background"

If you read through that one article you will already know a lot

of cosmology!

But several other people have said they like the

"Cosmology Tutorial" and the "Cosmology FAQ" at the

Ned Wright website.

He is a professor at UCLA who teaches cosmology and

also one of the leaders of the WMAP project.

I do not think one needs to read BOTH Lineweaver and Wright.

They are alternatives and the thing to do is find one that

explains things in the right way for you to understand.

Two women astronomers, Wendy Freedman and Siobahn Morgan, also

have online surveys and related material. Nereid may know more.

If you write a post requesting links to online introductory

accounts of cosmology----Nereid might answer and give good links.

Or some other people.

I guess my two favorite things are Lineweaver's article and

Ned Wright "Cosmology FAQ", but this might not be just right for you.

An Australian woman, Tamara Davis, has written a paper together with Lineweaver which is about the confusion and trouble people have understanding the expansion of the universe. The article is called "Expanding Confusion". I will find the link in case you are interested.

Dont work too hard. the thing is to find one article that works and read it patiently for a long time until it sinks in. Please keep asking questions! It helps keep the PF messageboard lively. We dont want Nereid to get bored and go away

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marcus

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If you can surround the system you are studying with an imaginary insulated box that does not let any energy in or out, or a kind of imaginary magic baggie that isolates the system, then you can apply the conservation law to what is inside.

It may be true that the universe is finite, but it may also not be true. So to be safe we should probably remember the law as not applying to the whole universe but to an isolated finite piece of it.

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The radius of the Universe is exactly the magnitude in light-years that it's age is in years.

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chroot

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That is certainly not correct.Originally posted by polarstarus

The radius of the Universe is exactly the magnitude in light-years that it's age is in years.

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It isn't? Why not?

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The particle horizon of the universe is believed to have a radius of 47 billion year lights. This is really greater that 13.7 billionsIt isn't? Why not?

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yes, that is greater than 13.7 although wrong. The correct figure is closer to 13.2.

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chroot

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I get the distinct feeling you don't really know what you think you know. Sorry. meteor is correct.Originally posted by polarstarus

yes, that is greater than 13.7 although wrong. The correct figure is closer to 13.2.

The reason the observable universe is larger than 13.7 Gly is simple: the universe wasn't always as large as it is today.

- Warren

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B: the ability to see beyond the radius is also affecting the data.

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Sorry. meteor is correct.

>maybe that is the belief, but not the fact

>maybe that is the belief, but not the fact

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marcus

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Polar replied: maybe that is the belief, but not the fact

--------------

there are two issues here: what do the pros say? what is

the consensus among mainstream astronomers about the radius of the

observable universe? (often called "the particle horizon"

which was the term Meteor used)

and then there is the other issue: do you have to believe them?

The clear answer to the second question is NO. You, PolarStarus, can believe it is whatever size. Everybody ought to feel free to imagine the universe however he likes.

But on the other hand you should make an effort to understand

the mainstream, and why they estimate the particle horizon at 47 billion LY at present. If you want to be unconventional, still try to understand the conventional view that you are differing from.

BTW there is some "give" in the number 47, it depends on exactly which set of parameters you use to calculate it but in all events it is around 47 or in the neighborhood of 45-50. Meteor can probably cite you a standard source for his number.

Warren teaches astronomy (I think he said as a sideline to his main carreer) so he may have more information bearing on this.

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marcus

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PolarS, here is something you might like to try:Originally posted by polarstarus

It isn't? Why not?

Ned Wright's or Siobahn Morgan's cosmology calculator.

two good online cosmology calculators:

Here are their homepages in case you want to see

who they are and what they look like (snap shots)

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

http://www.earth.uni.edu/smm.html [Broken]

and here are their calculators

Ned Wright's

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

Siobahn Morgan's

http://www.earth.uni.edu/~morgan/ajjar/Cosmology/cosmos.html [Broken]

I just tried Siobahn's (which I find easier to use) and got a result surprisingly close to Meteor's 47.

For very large, for practical purposes infinite, redshifts it said the present distance to the object is 46.1 or 46.2 etc billion LY.

That is for redshift 10 thousand and 100 thousand---the calculator said the distance is just a tad over 46 billion LY.

To get this kind of agreement you need to put in the current best estimates of the parameters.

In Siobahn's calculator, put in 71 for H (she has 70)

and put in 0.27 for Omega(matter)

and put in 0.73 for Lambda(dark energy)

after those preparations, whatever you put in for z (redshift)

you will get the presentday distance to an object which is now being observed to have that redshift.

the redshift of the cosmic microwave background is 1100.

very distant quasars have z = around 6

so those are things to plug in.

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One of the problems is this- Lambda isn't fixed, the accelration is decreasing in magnitude. The expansion rate will continue to increase but at an ever decreasing rate. The

acceleration was much higher in the early universe and goes to zero

as the age goes to infinity.

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chroot

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This sounds like abject speculation on your part. And it doesn't matter anyway -- the particle horizon is certainly larger than the age of the universe * c, regardless of acceleration (or absence thereof).Originally posted by polarstarus

One of the problems is this- Lambda isn't fixed, the accelration is decreasing in magnitude. The expansion rate will continue to increase but at an ever decreasing rate. The

acceleration was much higher in the early universe and goes to zero

as the age goes to infinity.

- Warren

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marcus

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Glad Siobahn's Dr. Who page meets with your approval! You describe the changes in the universe expansion rate over time and there is a plot of that in Lineweaver's Figure 14.Originally posted by polarstarus

One of the problems is this- Lambda isn't fixed, the accelration is decreasing in magnitude. The expansion rate will continue to increase but at an ever decreasing rate. The

acceleration was much higher in the early universe and goes to zero

as the age goes to infinity.

It is on page 30 of the whole PDF article

http://arxiv.org/astro-ph/0305179 [Broken]

but you can also get it from a Caltech website immediately without waiting for the whole 34-page article to download

I will get the direct link to Figure 14 "Size and destiny of the universe".

http://nedwww.ipac.caltech.edu/level5/March03/Lineweaver/Figures/figure14.jpg

or for a direct link including Figure 14 with caption

http://nedwww.ipac.caltech.edu/level5/March03/Lineweaver/Lineweaver7_7.html

One neat thing you probably noticed about Siobahn's calculator is that she gives the Hubble parameter H in past epochs. Like, what it was when the light the we are now seeing was emitted from a distant galaxy. As you suggest, PolarS, in past times like half billion or a billion years into the life of the U, the Hubble parameter (one measure of the expansion rate) was pretty huge, and for much of the life of the U it has been decreasing, as Figure 14 shows. But it may again be on the upturn. Anyway what they call the Hubble "constant" certainly has not been constant!

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Even if Omega was precisely equal to one, you could still have a finite universe: in this case, itsOriginally posted by marcus

However, if Omega is even slightly greater than one, then space may LOOK flat but on a very very very large scale (way greater than 14 billion LY) it may curve around on itself (analogous to a sphere surface) and be finite.

The Topology of the Universe by Boudewijn F. Roukema

Topology of the Universe: Theory and Observations by Jean-Pierre Luminet and Boudewijn F. Roukema

Cosmic Topology by M. Lachieze-Rey and J.P.Luminet

Topology and the Cosmic Microwave Background by Janna Levin

Constraining the Topology of the Universe by Neil J. Cornish, David N. Spergel, Glenn D. Starkman and Eiichiro Komatsu

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Nereid

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To be somewhat pedantic:Originally posted by polarstarus

One of the problems is this- Lambda isn't fixed, the accelration is decreasing in magnitude. The expansion rate will continue to increase but at an ever decreasing rate. The

acceleration was much higher in the early universe and goes to zero

as the age goes to infinity.

- a value for Lambda can be obtained from WMAP, SDSS, etc observations by making lots of model universes, with a wide range of values for Lambda (and Omega, and the proportions of cold dark matter (CDM - e.g. baryons, dark matter), hot dark matter (HDM - e.g. neutrinos), warm dark matter (??), etc, etc) and running statistical 'goodness of fit' analyses to determine the combination of parameters which best fit the data

- the values you see on sites such as WMAP's are those best fits, usually with errors quoted as 95% CLs (confidence limit)

- there are usually peer-reviewed papers which explain how all this modelling and statistical analysis was done, often in excrutiating detail (but sometimes irritatingly not)

Any, even all, the underlying theories may turn out to be wrong. However, they're the best of those seriously proposed so far. And they match the observations and experiments well.

Alternative theories are always possible - the Theory Development subforum has many - but they need to do at least as good a job in matching the observational data.

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Is there a reason why t-halo and t-disk seem to coincide with inflection points?