Finite universe and inflation theory

[honzik]

Hi,
I haven't found special topic about cosmology on this site so I hope this cathegory fits the best. The questions are:
1) Is cosmos(universe) finite or infinite? According to some articles I have read about inflation it seems that inflation theory works only with finite number of particles and finit space - where it "started". If this is not true (and the space is ininite - and also has infinite number of particles) has inflation "started" in the whole infinite universe at once - and not only in one specific "bounded" volume of space?
2) Can there be hypothetical possibility that conditions just before the inflation were similar to the conditions "inside" black holes? And if not - how do this condition (fundamentally) differ?

Thank you very much for any answers

Honzik

 

[Naty1]

Cosmology on this forum may be found at
https://www.physicsforums.com/forumdisplay.php?f=69

1) Is cosmos(universe) finite or infinite? According to some articles I have read about inflation it seems that inflation theory works only with finite number of particles and finite space.

No one really knows. I have never read that inflation theory leads inexorably to either finite nor infinite spacetime...There are many different inflation theories and many include bubbles where spacetime originates...these grow but maybe not fast enough to fill the inflationary "space" between them...I've forgotten how this problem was theoretically resolved...Our expanding universe has a cosmological horizon, and similar to a black hole event horizon, it marks the boundary to the part of the universe that an observer can see.

Wikipedia discusses global and local views at http://en.wikipedia.org/wiki/Inflation_(cosmology ) whre the local view is our causal observable universe...but not all that might exist!

2) Can there be hypothetical possibility that conditions just before the inflation were similar to the conditions "inside" black holes? And if not - how do this condition (fundamentally) differ?

yes, its possible but so far general relativity and quantum theory don't handle handle such singularities very well...they lead to infinities...whether such singularities are really "infinite" is an unresolved issue. No one knows the conditions at either the big bang, nor just before it if such a thing ever existed, nor inside black holes, but various theories provide limited insights.
There are other theories in which an endless cycle of universes occurs without beginning or end...when branes collide and finite spacetime is reborn...The Endless Universe by Paul Steinheirdt and Neil Turok explains one such theory based on Horava Witten heterotic M theory which includes ten dimensional spacetime between two infinite branes which bound our universe.

 

[Fredrik]

Roger Penrose likes to mention the fact that there's a fundamental difference between the initial singularity of the universe (the big bang) and final singularities (black holes and the big crunch). No one knows why, but the entropy of the universe was very small near the big bang.

 

[Naty1]

Post three makes a good point.

Seems to me inflation solves some problems like homogenetity, inhomogeneity and flatness, maybe even the absence magnetic monopoles, but it is a bit of a hodge podge theory... depending on things like some fine tuning and also on dark energy (for accelerating expansion as observed today) and likely dark matter in our current environment...not a completely coherent package...and most importantly, it is only a partial story, not one that explains the overall evolution of a universe...

Also, thinking a bit more about the size of the universe question, I probably should have mentioned that during inflation space itself expands faster than the speed of light...but is it infinitely fast? I don't think so, but if it is, even for a moment, the resulting universe predicted might be infinite; if not, seems like it would be finite for sure. Anyway, inflation theory was NOT promulgated as a determinant of the size of the universe. It is a "patch" to solve other problems which we can observe.

 

[humanerror]

This is sort of related, but I've been wondering about the "age of the universe" as it's estimated at 14.7 billion years. What can this number possibly mean in light of relativity, which does not offer an "objective" measurement of time? Is it 14.7 billion Earth years? What does it mean to measure distant galaxies and the expansion of spacetime itself in terms of Earth years?

This puzzles me so much, and I know it must have an answer because people much smarter than me cite that 14.7 billion years figure all the time. But what are they talking about?

 

[yogi]

Actually, its usually estimated to be around 13.7 billion - using the Hubble velocity distance law.

 

[yogi]

Once the Hubble constant is determined, then age follows consequent to the model used to describe the expansion - a decelerating universe leads to different results than an accelerating universe - and some universes such as the exponentially expanding de Sitter Universe, have no finite temporal beginning

 

[Chalnoth]

- and some universes such as the exponentially expanding de Sitter Universe, have no finite temporal beginning

Well, this isn't actually true once you add in the little complication that no universe is likely to be true de Sitter: there's going to be some small amount of matter around no matter what. And if there's even the tiniest bit of matter around, then as you go back further in time, eventually that sort of matter will get dense enough that it will overwhelm the cosmological constant.

So basically, as long as you assume General Relativity is valid, and that one can extrapolate backward in time indefinitely, you always get a singularity in the finite past. This tells us two things:

1. General Relativity must be revised under conditions of extremely high energy density.
2. There was a beginning. Perhaps not an absolute beginning of everything, but a beginning of any expanding region like our own.

 

[Carid]

1. General Relativity must be revised under conditions of extremely high energy density.

I have made this point before but never received any comment about it.

1. Inertia is a form of gravitational interaction.
2. Matter further away has more impact on the inertia of an object than matter close by simply because there is much more of it.
3. In the early universe the distribution of matter was rather different and the local matter may have played a larger role in inertia.

Can anyone find fault with these three points?

 

[Chalnoth]

I have made this point before but never received any comment about it.

1. Inertia is a form of gravitational interaction.
2. Matter further away has more impact on the inertia of an object than matter close by simply because there is much more of it.
3. In the early universe the distribution of matter was rather different and the local matter may have played a larger role in inertia.

Can anyone find fault with these three points?

Well, we do expect a quantum theory of gravity to modify its short distance behavior, which would include behavior in highly dense environments. But current experiments place the onset of any such modifications to General Relativity at higher energy densities than around 10^12 eV, and naive dimensional analysis places the onset of such modifications close to the Planck scale, or around 10^28eV.

 

[honzik]

1) Is cosmos(universe) finite or infinite? According to some articles I have read about inflation it seems that inflation theory works only with finite number of particles and finite space.

No one really knows. I have never read that inflation theory leads inexorably to either finite nor infinite spacetime...There are many different inflation theories and many include bubbles where spacetime originates...these grow but maybe not fast enough to fill the inflationary "space" between them...I've forgotten how this problem was theoretically resolved...Our expanding universe has a cosmological horizon, and similar to a black hole event horizon, it marks the boundary to the part of the universe that an observer can see.

Let's return into the first question - whether the universe (cosmos) is or isn't finite. This discussions supposes that phenomenon called inflation took place and that inflation "spread" in time - ie. that it started somewhere (in one place or in infinite places) and subsequently (at finite speed) the effect of inflation influenced surrounding places. Let's discuss the alternative that cosmos is not finite - because here we will (I think) get into some trouble.

a) Let's suppose that inflation was "started" at bounded volume in (infinite) space. It then follows that:
I) inflation still continues in some place in the universe (as it spreads more and more from the place where it started) - because space is infinite and the speed of inflation was (is) finite
or II) inflation ended some time ago. But in this case there has to be some (infinite) space in the universe not influenced by inflation simply because the effect of inflation didn't reach this place (inflation took finite time and spread in finite speed) - but this can imply that space is not homogenous (in places which inflation didn't reach). And maybe it can imply some other hard to explain difficulties that a better knowledged cosmologist can explain.

b) Let's suppose that inflation started in the whole infinite universe at approximatelly the same time. (In case it stated in the "half" of the universe - yet still infinite half - we will be at the same situation as in points aI) and aII).). But this point seems really strange - how could be inflation started at (approximatelly) the same time on the "opposite" (or better to say very very far - arbitrary far) places of the universe? How should these "opposite" places "know" that they had to start with inflation? And even if the inflation started in the whole infinite universe at the same time - there could be problem (as I nave read somewhere) with homogenity of the universe after inflation.

c) The most interesting (and crazy) idea: the cosmos was finite before inflation and after inflation it was infinite - which seams to me really unbelievable.

d) The whole inflation is just one quantum "change" (but I don't specify exactly the details) of one particle one one other quantum entity - that took place at one time all over the universe (quantum effects can show this behavior, i think).


Can you please tell me which of these ideas could (theoretically and reasonably) happen and which ones are only pure speculations with no theory (known up to today) behind them or that are in contradiction in some reputable theory?

Thank you very much for your answers.

Honzik

 

[Chalnoth]

Well, if the universe is infinite, there's no reason why inflation must start everywhere at once. In fact, it's basically impossible due to speed of light limitations. Instead what you'd get is little pockets of the infinite universe that start inflating.

 

[Naty1]

You simply cannot link current inflation theory to the size of the universe...inflation cures homogeneity,inhomogeneity and flatness problems...it does not define the size of the universe ...

 

[honzik]

Well, if the universe is infinite, there's no reason why inflation must start everywhere at once. In fact, it's basically impossible due to speed of light limitations. Instead what you'd get is little pockets of the infinite universe that start inflating.

To be able to discuss about inflation we have to define what we understand under the term inflation. Or to be less strict - what are the exhibitions of inflation.

The first and major question of all is:

Does inflation take place in the whole universe (no matter whether it is finite or infinite)?

 

[TalonD]

Roger Penrose likes to mention the fact that there's a fundamental difference between the initial singularity of the universe (the big bang) and final singularities (black holes and the big crunch). No one knows why, but the entropy of the universe was very small near the big bang.

What is entropy exactly?

 

[Chalnoth]

What is entropy exactly?

A number proportional to the logarithm of the number of microstates that can replicate a given macrostate.

 

[Chalnoth]

To be able to discuss about inflation we have to define what we understand under the term inflation. Or to be less strict - what are the exhibitions of inflation.

The first and major question of all is:

Does inflation take place in the whole universe (no matter whether it is finite or infinite)?

What you are asking, it seems to me, is whether the inflation that started off our own patch of the universe started off everything, or whether other inflation events occurred as well. First, we just don't yet have the information available to us to answer this question. However, it seems to me that if inflation started once, it likely has started many times. A one-off inflation event seems naively unlikely.

 

[honzik]

What you are asking, it seems to me, is whether the inflation that started off our own patch of the universe started off everything, or whether other inflation events occurred as well. First, we just don't yet have the information available to us to answer this question. However, it seems to me that if inflation started once, it likely has started many times. A one-off inflation event seems naively unlikely.

But whether inflation occurred once or miltiple times - every occurence concerns, I ithink, only finite space in the universe. Because than we can get into trouble - so: can inflation affect the whole infinite universe (if the universe is infinite) - and if the answer is yes - how can the places all over the infinite universe know that they have to start inflation at that time?

 

[Chalnoth]

so: can inflation affect the whole infinite universe (if the universe is infinite)

No, because that would violate the speed of light limitation.

 

[honzik]

can inflation affect the whole infinite universe (if the universe is infinite)

No, because that would violate the speed of light limitation.

That's important point from which we can deduce further away: Then - if the space is infinite - some scenarios could happen:

1) There was only one "seed of inflation" (call it inlation F) where the space inflated - let's call this inflated space I (it includes all the space in universe we can see today) and the region outside this inflated space - let'ca call it space S - is still "the same" as it was before the inflation F (ie unaffected by inflation). Than the questions are - what are the conditions in space S today? What are the conditions on the border of spaces S and I? By conditions i mean basic structure of the space and fields.

2) There were several (maybe infinite) seeds of inflation Fi taht inflated spaces Si (i is an index). Then the question is what are the conditions on the border of neighbour spaces Si?

Well, these question are hard to answer because no one can observe that mentioned spaces but what does the theory say about these questions? Could these scenarios even happen - according to inflation theory - or does inflation theory imply finite space?

Thank you.

Honzik

 

[skippy1729]

Since there are inflation models for both finite and infinite universes it seems unlikely that inflation will settle the question. A real possibility is that the size of the universe will narrow the field among competing inflation theories. It might be determined the old fashioned way--experimentally. Many groups around the world are sifting the CMB and galaxy distribution data for evidence of a finite universe with a closed topology.

For introduction see: Scientific American Volume 12 Number 2 2002 special edition "the once and future cosmos"; specifically "Is space finite" by Luminet, Starkman and Weeks. "The Shape of Space" by Jeffrey Weeks is also excellent.

 

[marcus]

Since there are inflation models for both finite and infinite universes it seems unlikely that inflation will settle the question. A real possibility is that the size of the universe will narrow the field among competing inflation theories. It might be determined the old fashioned way--experimentally. Many groups around the world are sifting the CMB and galaxy distribution data for evidence of a finite universe with a closed topology.

For introduction see: Scientific American Volume 12 Number 2 2002 special edition "the once and future cosmos"; specifically "Is space finite" by Luminet, Starkman and Weeks. "The Shape of Space" by Jeffrey Weeks is also excellent.

Skippy I agree. Finite/infinite is more likely to be decided by observation.
The latest WMAP report on cosmology has a 95 percent confidence interval on a parameter which if it is negative would make U spatially finite. That will be narrowed down by Planck mission. The confidence interval could eventually be all on the negative side of zero which would settle it.
http://arXiv.org/abs/0803.0547
Look in Table 2 on page 4. The interval is [-0.0179, 0.0081]
You can see it is more on the negative side. If it goes all negative then space is finite.

Reasoning about finite/infinite on the basis of assumptions about inflation (as some are trying to do) doesn't work because inflation is such a nebulous concept, so many different scenarios, and it involves freely made-up stuff.

But like you say if finite/infinite can be determined by observation then that would help favor some inflation stories and disfavor others. "Narrow the field."

You might want to provide links to the SciAm articles you are recommending, to make it easier and encourage more people to read them. It's more trouble but I think it works.

 

[skippy1729]

Link to Scientific American article
http://cosmos.phy.tufts.edu/~zirbel/ast21/sciam/IsSpaceFinite.pdf

"The Shape of Space" by Jeff Weeks is one of those old fashioned things made from dead trees. It should be in most good libraries. His website http://www.geometrygames.org/CurvedSpaces/index.html has a cool download (Windows, Mac or Source Code, no Linux) that simulates dozens of multiply connected spaces.

Skippy

 

[Entropee]

So does an expanding universe also cause an increase of entropy?

 

[Chalnoth]

So does an expanding universe also cause an increase of entropy?

Yes. Basically the entropy of a region of the universe is given by its horizon size. The smaller the Hubble parameter, the larger the horizon. As the universe expands, the Hubble parameter decreases, leading to a larger horizon, and thus higher entropy.

 

[Entropee]

Yes. Basically the entropy of a region of the universe is given by its horizon size. The smaller the Hubble parameter, the larger the horizon. As the universe expands, the Hubble parameter decreases, leading to a larger horizon, and thus higher entropy.

so is there a lesser chance of galaxys forming in the future as it increases?
and other examples like that.

 

[Entropee]

also this paper says otherwise... http://adsabs.harvard.edu/full/1991Ap&SS.186..157U
and so do many other sites.

 

[Chalnoth]

so is there a lesser chance of galaxys forming in the future as it increases?
and other examples like that.

Well, yes, but that doesn't have much to do with the expansion of the universe. Basically what happens is that eventually all of the gas that is out there will end up in stars, all of which will be either white dwarfs, neutron stars, or inside black holes. Eventually even those will collide or decay, leaving nothing but black holes. Those will then evaporate away through Hawking radiation, and all we'll have is empty space.

This Wikipedia article is a fairly good introduction to this topic:
http://en.wikipedia.org/wiki/Future_of_an_expanding_universe

 

[Chalnoth]

also this paper says otherwise... http://adsabs.harvard.edu/full/1991Ap&SS.186..157U
and so do many other sites.

Okay, that paper is positively ancient where cosmology is concerned. And it's simply wrong for the cases that we know how to calculate accurately, namely a de Sitter universe with a black hole inside: in such a universe, the de Sitter universe (i.e., one with a positive cosmological constant) has a lower entropy if there is a black hole inside it than if there is nothing but empty space.

Furthermore, it's been shown that for a given enclosed mass, a black hole has the highest entropy possible. This makes sense given that what we know of physics today has our universe (over very long time spans) transitioning to nothing but black holes, and then just empty space as those evaporate.

While it is true that there are a number of calculations that we just don't know how to perform that are required to define the entropy of the current and past universe, a universe that is vastly more complicated than black holes and empty space, I think we have enough information available to us to state categorically that the entropy of the universe as a whole is increasing.

 

[Entropee]

>.< Man I am still not so sure because i started a thread on it and someone else explained pretty well how it stays the same because of cooling objects.
But yours makes a lot of sense too.