Universe Is Infinite: Mathematical Proofs

[Moni]

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?

 

[mathman]

There are lots of theories about the universe, but none, as far as I know have the universe of infinite size. In any case, the maximum we can see is about 14 billion light years. Moreover there are lots of figures (I can't quote them) which describe how much stuff there is in the unuverse.

 

[marcus]

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?

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.

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
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
"Inflation and the Cosmic Microwave Background"

Michael Turner
"Making Sense of the New Cosmology"
http://arxiv.org/astro-ph/0202008

Wendy Freedman and Michael Turner
"Measuring and Understanding the Universe"
http://arxiv.org/astro-ph/astro-ph/0308418

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 into 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.

 

[marcus]

Cosmology Resource Sticky Needed

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
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.

 

[marcus]

more stuff for the cosmology resource sticky

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

homepage for Siobahn in case you want to see who she is
http://www.earth.uni.edu/smm.html
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

----------

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

----------

 

[marcus]

more stuff for a cosmology resource sticky (if we ever get one)

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 0.43 quintillion seconds.
Except they don't say 0.43 quintillion seconds they either express the Hubble time in years (something like 13.8 billion) or they use traditional astronomer mongrel units and say it is "71 kilometers per second per Megaparsec."

So what does this mean about the density of energy in the universe?
It is good to have a rough idea of the extent of the universe but also an idea of the density of energy----how much joules per cubic kilometer, or cubic mile, or cubic lightyear is in it.
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" = 3c²H²/8piG

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.

 

[Moni]

Originally posted by marcus

Is Chittagong in Bangladesh?

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

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

We all know from laws of thermodynamics:

Energy can be transformed from one type to another
Total amount of energy in the universe is constant

We also know that universe is full of mass, particles that means energy!

And if the the universe is infinte, then, the total amount of energy in the universe is also infinte...which is not constant

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 :)

 

[marcus]

Moni, I am so glad you stayed around. I was afraid you
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 don't want Nereid to get bored and go away

 

[marcus]

Moni, the conservation of energy law does not have to apply to an entire finite universe. It can be applied to an isolated PART of the whole thing.

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.

 

[polarstarus]

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

 

[chroot]

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

That is certainly not correct.

- Warren

 

[polarstarus]

It isn't? Why not?

 

[meteor]

It isn't? Why not?

The particle horizon of the universe is believed to have a radius of 47 billion year lights. This is really greater that 13.7 billions

 

[polarstarus]

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

 

[chroot]

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

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

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

 

[polarstarus]

A: Any data pointing to larger than 13.2 is skewed by spacetime curvatures(or just wrong) and
B: the ability to see beyond the radius is also affecting the data.

 

[polarstarus]

Sorry. meteor is correct.

>maybe that is the belief, but not the fact

 

[marcus]

Warren (chroot) said: Sorry. meteor is correct.

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.

 

[marcus]

Originally posted by polarstarus
It isn't? Why not?

PolarS, here is something you might like to try:
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

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

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.

 

[polarstarus]

I like her Dr. Who page.
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.

 

[chroot]

Originally posted by polarstarus
I like her Dr. Who page.
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.

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).

- Warren

 

[marcus]

Originally posted by polarstarus
I like her Dr. Who page.
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.

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.

It is on page 30 of the whole PDF article
http://arxiv.org/astro-ph/0305179
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!

 

[cragwolf]

Originally 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.

Even if Omega was precisely equal to one, you could still have a finite universe: in this case, its topology would have to be multiply-connected. For example, a 3-torus, a kind of 3-dimensional version of the surface of a doughnut, is flat everywhere, but its volume is finite. General relativity (and hence the standard big bang model) has nothing to say about topology. Perhaps this is a limitation, perhaps not. Anyway, here are some articles on the subject of cosmic topology:

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

 

[Nereid]

Originally posted by polarstarus
I like her Dr. Who page.
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.

To be somewhat pedantic:
- 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.

 

[polarstarus]

Question on Lineweaver's Chart

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

 

[marcus]

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

PolarS, I missed seeing your question earlier and just now realized it was there!
I don't see any connection but that's no proof there isn't one!
(I don't even see them occurring at inflection points! still have to look more at this figure and study the caption I guess)
have to go out now but will look later and see if there's
some relation
----------------------

I'm back after a night's sleep and can edit in some comments on
the t-halo and t-disk stripes.

They are not essential to the Figure, but something Lineweaver added to show "the tightening network of constraints" as it says in the caption beneath the figure.

The point is that this curve---most likely the heavy solid curve (0.27, 0.73) is the right one----is what relates time in years to redshift.

there is a strict invariable connection between "size of universe" and redshift---they are the same scale with different labels so you see them in the figure drawn on the LHS and the RHS of the figure as alternative y-axis scales.

So the curve relates time in years to the size of universe and therefore to redshift.

But within our own galaxy we can measure ages of stars by their spectra! Stars that formed early have less metal, and less different colors. So we can tell how long ago, in years, the disk formed and the halo formed. Disk formed 9 billion and halo formed 12 billion years ago, say.

Now let us assume that all galaxies formed at about the same epoch.
So we can TEST our curve to see if it is reasonable!
The curve predicts what redshifts correspond to 9 billion and 12 billion. It says about z =1 and about z = 4, say. So to perform the test, we look back at galaxies with z = 1 and see if they are forming their disks.
And we look back at galaxies with z = 4 and see if they are forming their halos.

The picture shows a good fit for the heavy solid curve. If you put your finger at z = 1 on the redshift scale and move horizontally until you reach the curve, you will hit the curve at right about over the 9 billion years ago spot. Likewise for z = 4, you hit the curve right about the 12 billion years ago. So observing galaxies at z = 4 in haloformation stage, which I guess they do, tends to confirm that curve.

No big deal but reassuring

 

[polarstarus]

It's actually kind of hard to tell from this chart, but it sort of looks like t-disk corresponds to an inflection point on the bold continuous line,(0.27,0.73), and t-halo to the light continuous line,
(0.1,0.9). He says that the bold line is the best-fit for the data. In any event an inflection point on the size graph has to have implications. What would have caused the change? My model has no inflection points, but is always upwardly concave.


Re: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

Interesting, what about omitting dark matter?

Re: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.

I predicted 13.2 for the age when everyone was saying 15, and also an acceleration in the expansion. There are some other correlations, but these have provided impetus for further exploration of my current model.

 

[marcus]

more for the source material sticky

We don't have a sticky thread for cosmology links----the "useful source material" sort of thread. So I've begun using this thread as a sticky surrogate. There are cosmology tutorials and links to cosmology calculators and articles about dark matter and so on.

Here's a link to an especially good PF thread about the expansion of space. It is wideranging and touches on a bunch of cosmology and general astronomy type issues. Nereid has a good short essay on dark matter.

https://www.physicsforums.com/showthread.php?s=&postid=135705#post135705

Here are some more links that Nereid supplied (astronomy/cosmology sources) in another thread:

"...This page, brought to PF members by ranyart, is a good place to start:
http://www.solstation.com/x-objects/greatatt.htm
...
...

I don't have any good ones immediately to hand. However, this site has many excellent links:
http://msowww.anu.edu.au/2dFGRS/

In particular, this paper gives a flavour of how the work is done: "The 2dF Galaxy Redshift Survey: Cosmological Parameters and Galaxy Biasing", Ofer Lahev, in astro-ph/0205382

A couple more:
http://antwrp.gsfc.nasa.gov/apod/ap011219.html
and if you click on the 'computer simulation' link in this page, you will get...
...
...

A pretty picture:
http://antwrp.gsfc.nasa.gov/apod/ap030611.html
...
..."

 

[Phobos]

Originally posted by marcus
We don't have a sticky thread for cosmology links----the "useful source material" sort of thread.

https://www.physicsforums.com/showthread.php?s=&threadid=13306"

 

[Ontoplankton]

When cosmologists say there are theoretical reasons from inflation theory why the universe has to be exactly flat, do they mean exactly flat and truly infinite, or just very close to exactly flat and enormously large (compared to the Hubble scale)?

I know that inflation is supposed to blow everything up by a factor of 10^oodles, but that doesn't make anything infinite, just huge.

So does it have to do with eternal inflation being eternal, so that it becomes possible to make the universe infinite by choosing a different time coordinate, as described here? If so, is it really true that inflation has to go on forever in most models? (Is all inflation eternal inflation?)

Or do they mean other reasons? Or is it just a sloppy way of speaking? Or am I confused?

If anyone can answer this, thanks.

 

[marcus]

Inflation scenarios work equally well starting from an infinite universe or a finite universe. All inflation scenario needs to do is expand space by a factor of exp(60) or so, which it can do starting from an infinite space or a finite one.

Cosmologists do not know that inflation occurred. It is so speculative that the word "scenario" is used instead of "theory".

Flatness or near-flatness is observed.
Inflation is a speculative scenario proposed to explain some observed facts, like flatness.

Q:When cosmologists say there are theoretical reasons from inflation theory why the universe has to be exactly flat, do they mean exactly flat and truly infinite, or just very close to exactly flat and enormously large (compared to the Hubble scale)?

The observations can't distinguish between infinite (which is certainly simpler!) and finite with slight positive curvature but very very big.

All the observations can do is say Omega = 1.02 +/- 0.02, the current best estimate. If in fact Omega is exactly one (which would be nice and simple) then the U is infinite and flat. If instead Omega is 1.01 or 1.03 then the U is finite.

For now all we can do is measure Omega and narrow down the uncertainty about it as instruments get better.
This is all IMO and AFAIK.



Q:I know that inflation is supposed to blow everything up by a factor of 10^oodles, but that doesn't make anything infinite, just huge.

That is right. the expansion factor that people talk about is exp(60) or "60 e-foldings". That is only 10 to the 26 by my calculator so it is not THAT big. Infinite expands to be infinite and finite expands to be finite.

Q:So does it have to do with eternal inflation being eternal...

Does what have to do with inflation being eternal? As far as I know "eternal inflation" scenarios are really speculative. They are fantasies about how things could be without empirical substance to them. In reply I would say no. Nothing has to do with inflation being eternal. However the scenario of eternal inflation can be used to generate gorgeous computer graphics, as Andrei Linde and others have done.

there is a trick to this however. Lee Smolin has proposed a Darwinian explanation of why the physical constants like 1/137 are so nice. this explanation depends on their having been many generations of
spacetimes with slightly different physical constants which means slightly different physical laws (the constants are the coefficients in the laws of physics so different constants means differnt laws).
the values of the constants have evolved so that they confer "reproductive success" to the universe by encouraging the condensation of gas into stars and stars into black holes, which bud out the backside to form offspring spacetimes. those worlds with the most conducive constants reproduce more. so the ensemble of all worlds consists largely of those with physical constants which encourage black hole reproduction. Smolin uses this to explain why numbers like 1/137 are what they are. They are incidentally also supportive of our kind of life but that is just a tangential byproduct and not part of Smolin's story.

this is an intelligent speculation but it has nothing to do with finitude or infinitude of individual spacetimes, so it is not relevant to your question.

the best introductory cosmology paper I know is Lineweaver "Inflation and the Cosmic Microwave Background"
http://arxiv.org/astro-ph/0305179

and his Figures 4 and 5 are about inflation. On pages 10-13 he discusses it as a way of addressing the flatness problem and the horizon problem

 

[Ontoplankton]

Marcus, thanks for your reply. If I'm understanding you correctly, you're claiming that the only theoretical reason why an inflationary universe should be exactly flat is that this is simpler than an almost exactly flat universe. Wouldn't this mean that inflation theory makes an infinite universe less likely, rather than more likely? If omega has a value close to but not equal to one, wouldn't that be a bigger coincidence in a non-inflationary universe than in an inflationary universe, considering that inflation brings omega to near one from wherever it started out?

Also, are you saying that eternal inflation is (much) more speculative than inflation itself? They do claim in the paper I linked above something like "a generic feature of inflationary models is that inflation goes on forever". They also claim this means that the universe is infinite "seen from the inside" (for one choice of coordinates).

 

[marcus]

Originally posted by Ontoplankton
Marcus, thanks for your reply. If I'm understanding you correctly, you're claiming that the only theoretical reason why an inflationary universe should be exactly flat is that this is simpler than an almost exactly flat universe.

I should not have given that impression. Sorry if I was careless or overly simple! People do give theoretical reasons and plausibility arguments why the universe should be exactly flat (since it is approximately). I tend to discount what seems to me primarily theoretical reasoning and put more faith in observation but that is a personal bias perhaps. Simplicity is not the only reason. People who want to find theoretical reasons can find others. All I believe is that omega is tantalizingly close, if not exactly, equal to one.
I believe the 1.02 +/- 0.02 and even that involves a leap of faith since one has to trust the people using the instruments.

Originally posted by Ontoplankton
... Wouldn't this mean that inflation theory makes an infinite universe less likely, rather than more likely? If omega has a value close to but not equal to one, wouldn't that be a bigger coincidence in a non-inflationary universe than in an inflationary universe, considering that inflation brings omega to near one from wherever it started out?

YES! You are absolutely right about that. Inflation scenarios are attempts to solve among other things "flatness problem" and the "horizon problem". Without imagining inflation it would be extremely difficult to see how the U could be so flat without having started out 100 percent flat. Because ordinary expansion (in a matter or radiation dominated U) exaggerates curvature. While, as you say, dark energy dominated expansion flattens out curvature.

You know all about this. If you didnt already know, that Lineweaver article explains the nuts and bolts of it with a few simple equations
on page 11 and 12. It is such a good pedagogical article! Makes the mechanical details of it simple and understandable.

Originally posted by Ontoplankton

Also, are you saying that eternal inflation is (much) more speculative than inflation itself?

I am not certain what you mean by "eternal inflation". I will post what I have so far and think about it.

 

[marcus]

two notions of eternal inflation

inflation scenarios normally have some kind of "graceful exit"
by which they imagine that inflation stops of its own accord after some fraction of a second during which the 60 e-foldings happen.

Lineweaver discribes this.
--------------

It seems to me that "eternal inflation" could mean two things.

One is Andrei Linde idea (adopted by others such as Lee Smolin, who puts it to Darwinian evolutionary use).
Andrei Linde likes to imagine universes budding off of universes, like cactus. Well that is not the only image of it. I am not a good one to explain this. But perhaps it should be called "endlessly REPEATED" inflations. or endlessly repeated big bangs. Universe after universe comes into existence as an expanding bubble or expanding bud from some prior entity.

this is actually a poetical idea. some ideas are so appealing to the psyche that they develop a power that transcends scientific scrutiny and evaluation. I will not be such a curmudgeon as to say that Linde's idea is bad because it is speculative. I like it because it is excellent and visual poetry.

But (because it contemplates a large number of individual universes, connected by impenetrable bigbang budding events or like oases separated by untraversable deserts) this IS more speculative than simply picturing an inflation scenario lasting some fraction of a second at the beginning of the universe which we witness and belong to.

The customary inflation scenario that people invoke is a brief one-shot episode that is assumed in order to explain two or three things about the world we see.

Endlessly reiterated inflation is a different story.

THE SECOND MEANING of "eternal inflation" might be just inflation that goes on for ever.
that is not a feature of the usual bigbang inflation scenario but
one could give meaning to the idea

One could say that "inflation" by definition is any expansion which accelerates due to the neg pressure of a vacuum energy term or a cosmological constant.

For most of the history of the U, according to the mainstream view, expansion has been slowing down.
Lineweaver has a picture of this. Figure 14 "the size and destiny of the universe"

But starting a few billion years ago the dark energy term began to dominate and expansion began to speed up. You will see in Figure 14 an inflection point where that happened.

Figure 3 shows how a matter dominated U (decelerating expansion) can give way (as matter thins out) to a dark energy dominated U (accel. expan.)

So you can say that as of a couple of billion years ago we are in a new inflationary stage and we see no end to it
(the only "graceful exit" would be if the dark energy term would decrease and people play with models in which the cosmological constant does change---but there is no observational evidence that it changes so that is so-far just model-play)
Thus you could say we are not in an "eternal inflation" era that began a couple of billion ago.

But we can not really say that it is going to be eternal because we don't know if Lambda changes or not. And anyway what is going on now is not what people usually mean by an inflation scenario.

I get the idea this is familiar ground to you---but am spelling things out like this partly to provide you an opportunity to disagree if you have different ideas.

 

[marcus]

Onto, I had some comment on the paper by Garriga and Vilenkin
that you linked to, but withdrew it as too argumentative.