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Expansion of the Universe question 
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#1
Apr711, 09:15 PM

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Okay, I'm not a physicist/cosmologist, but I was wondering about the expansion of the universe. Current theories suggest that heat death is the ultimate fate of the universe. The energy of the universe becomes diffuse to the point of irrelevancy as time approaches infinity. This is due to the observed acceleration of the expansion of the universe.
But as any kid who's been through intro physics can assert, there's more to kinematics than just velocity and acceleration. Is the rate of acceleration of the universe a constant, or is it too a variable? Could the acceleration itself be decreasing over time, leading to the scenario where the universe's acceleration becomes static (briefly leading to a dynamic equilibrium where the expansion of the universe is at a constant velocity) and subsequently begins to accelerate negatively, I.E. contract? I hope someone can clear this up for me. 


#2
Apr711, 09:55 PM

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Current observations show that the expansion is accelerating.



#3
Apr711, 10:10 PM

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Cosmologists don't have certainties. All they can do is fit model to datafind the simplet model that gives the best fit.
It's a great field because new (space and ground) instruments are supplying a river of data including completely new kinds (neutrino, gammaray...) and because the models are elegant and arise from our theory of gravty (Gen Rel) and its evolving geometry. But merely being in an exciting field does not mean they can answer ultimate questions with certainty. What is accelerating is the scalefactor a(t) and there is an equation called Friedmann eqn that tells how the derivative should changed. It tells you a'(t). http://en.wikipedia.org/wiki/Friedmann_equations And there is also an acceleration equation that determines how the second derivative a''(t) should behave. These equations have constants Lambda and (sometimes also ) w in them. They themselves are not the acceleration but they determine how the acceleration should behave according to the model. A lot of work has been going in to measuring the best fit values of Lambda and w. And checking to see if they change over time! So far there is no evidence that those two constants are changing! this leads to the tentative conclusion that the U will keep on expanding (in a rather sedate way) The model is supported by masses of data and it fits the data extraordinarily well so this lends confidence. Plus the best we can tell by bestfit values of Lambda and w, they are constant. But there are errorbars, uncertainties. So one suspects they are constant, at least that is consistent with the data. Future data from even better instruments might indicate differently and some variation over time might be discovered, but tentatively for now it looks like continued expansion. Wikipedia has an article on "Friedmann equations" that includes the acceleration one. I checked the article http://en.wikipedia.org/wiki/Friedmann_equations and it only had the one constant Lambda. The presentation was simpler than some others I remember seeing, that had a "dark energy equation of state w". But that's OK. Maybe w is an unnecessary complication and the Wikipedia treatment gets the basic idea across. 


#4
Apr711, 10:18 PM

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Expansion of the Universe question
Thank you, that's just what I wanted to know!



#5
Apr2211, 01:04 AM

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#6
Apr2211, 01:29 AM

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#7
Apr2211, 03:05 AM

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Words easily get mired in confusion. the scalefactor a(t) has a definite meaning and increases according to a set equation. the acceleration is a"(t) If you google "Friedmann equations" and look at the Wikipedia article about them you will see that as the universe expands and the density goes down you get both a'/a and a''/a tending to constant valuesclosely related constants in fact. Those are two basic facts and you can draw simple plots to show how typical distances are expected to grow. But may be hard to say in words. there is no one speed that the U is expanding with. Different distances expand with different speeds. But there is a unique unambiguous meaning to a(t) and a'(t) and a"(t). I guess the gradual convergence to constant ratios really signifies steady exponential growth of the scalefactor, in the limit. 


#8
Apr2211, 08:21 AM

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#9
Apr2211, 09:32 AM

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Hi A.C., now I am in deep trouble! I had the "bright" idea to try to shift over from ordinary language words, in this discussion, to mathematically welldefined concepts like the scalefactor.
It's true that the scalefactor could stop increasing and start declining, but it would need some new physics that we have no evidence for. We have to be open to the idea. But for now we have a standard model that fits the data remarkably well. It's good to understand that, at leasts as a provisional starting point. According to that standard model, cosmology is based on the Friedmann equations (google those two words) with a small positive constant Lambda. those two equations govern the scalefactor. One equation governs a'(t) because it gives you an expression for (a'/a)^{2}. It says it equals a term that goes to zero in the long run (as density declines) plus a constant term proportional to Lambda. So the ratio a'/a eventually levels out to a constant. The other equation governs a''(t) because it gives an expression for a"/a. It says that a"/a equals a negative term that goes to zero in the long run (as density declines) plus a constant term proportional to Lambda. My dilemma is that I'm not sure how to say those two things in words that I can trust everybody to understand. The model clearly says that all three quantities continue increasing indefinitelya and a' and a" continue to grow. But that doesn't matter as much as what happens to their ratios! The model tells us that a'/a levels out to a constant. You can think of a'/a as the fractional expansion rate of distances. Longer distances grow by more in a given period of time. a'/a tells you by what fraction of its total length a distance grows in a given time. That fractional growth rate goes to a constant value in the long run as density goes to zero. Maybe the way to say it is to appeal to the idea of compound interestexponential growthsomething everyone is familiar with. If you google "Friedmann equations" and look at the wikipediia article what you see is basically exponential growth plus another term that gets less and less important as density goes to zero. The long term shape of the scalefactor curve is an exponential. I'm worried now that having introduced the scalefactor into the discussion will only cause confusion. I think the explanation problem is that as far as we know there is no standard speed in miles per hour that the U is expanding at. Instead there is a fractional growth rate of distances. Maybe it is better to think of it as a "savings account interest rate" rather than a "miles per hour" speed. Let me know if I'm just making things murkier and more confusing. 


#10
Apr2211, 12:04 PM

P: 366

Great explanations as always Marcus, if the growth rate is exponential, exponential gorwth rates are infinite, which is funny because if U does have an exponential expansion rate based on distance, then if you could "pause" existence and move around infinity it would still be homogoneous which seems almost paradoxical.
That being said that would make sense that heat death would happen infinitely (at all points in time and space) eventually assuming U is isotropic, as models dictate. Your opinion on this is valued. 


#11
Apr2211, 01:05 PM

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Thanks for the encouragement. (I'm not sure I understand but) I think you are exploring the question of whether the standard model U is spatially finite or infinite.
I don't have an opinion either way on that. Also my nonexpert opinion would not count for much (I'm just a retired mathematician who got interested in cosmology late in life.) My personal taste, which shouldn't make any difference, is towards a spatial finite* version. But the standard model (incidentally the technical name for it is LambdaCDM) comes in both finite and infinite versions and there is a chance that within our lifetime it will be decided which is the better fitthe data keeps getting more and better. *with a slight positive spatial curvature, making the 3D space curve around and form a hypersphere, the analog of an ordinary 2D spherical surface. Infinite is consistent with the data, and also a (very large, only slightly curved) finite version is consistent with the data. There's an error bar. The data is not yet good enough to distinguish. I'd be glad to see it resolved either way. I'm sure we all realize that models are only provisional and approximate. They get revised and improved with time. They really aren't meant to be "believed" they are just meant to be provisionally used to fit data to, and have their predictions tested, and eventually get improved on. Probably the biggest potential for change is in the area of quantum cosmology (QC) where research is proceeding on ways to eliminate the singularity at the start of expansion and extend the model back in time. The challenge there will be how to test an extended LambdaCDM that goes back prebang. I recently did a search at the (German mirror of) StanfordSLAC database that turned up 41 recent papers discussing ideas for tests of an extended cosmology that resolves the singularity. These are mostly too technical to read, for the most part, but I will share them with you in case you want a taste of work in progress. These are papers which have appeared in 2008 or later: http://wwwlibrary.desy.de/cgibin/s...tecount%28d%29 The very last one, #41, happens to be about Penrose circles. This list is not exhaustive in any sense, but it is all about testable cosmology where the bang is resolved/replaced and time extends back. 


#12
Apr2211, 03:05 PM

P: 366

Marcus,
Yes I was exploring the idea of spacially finite/infinite space. Thankyou for the links to papers however I am an IT technician so my maths is sketchy at best! Personally I just find the idea of infinite matter time/space paradoxical to the proven acceleration of spatial expansion, at an instinctive level, (I understand this can not be offered as a valid point of logic). Well I do until I thought of a comment someone on here made how geometry dictates the BB begain at all points in space which then makes me think infinite mass/energy is implied. If the U had infinite mass/energy though then how could it ented a heat death? Because of its entropy and isotropy? I have looked at hyperspheres and although I dont understand the mathematical model i think they make more sense, as infinity is a hard pill to swallow. So I can see your viewpoint there. That being said I am not assuming that this finite U is the totality of everything, there maye be U3,U2,U1,U+1,U+2,U+3, if you understand my meaning. I am not endorsing 'multiverse' theory or anything of the sort but just from general reading of this forum I see there is QM and other theories that has pre big bang/an infinite of finite U models  whether any of this is proven or accepted I would not know. Thanks for you reply. 


#13
Apr2211, 04:05 PM

P: 61

Nothing can approach infinity. There are theories that predict the universe will expand to a point and then contract itself. Some theorists think that multiple big bangs occur this way.



#14
Apr2211, 05:45 PM

P: 366

Or am I missing your point? Thanks 


#15
Apr2311, 06:37 PM

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#16
Apr2411, 04:02 AM

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One thing I've missed in this is: What is fueling the acceleration?
Is it energy left over from the BB? If so, what form does that energy take? As a layman, I think of energy in its potential and kinetic forms  kind of like petrol/gasoline  once transformed or ignited, it reaches velocity quickly and doesn't keep accelerating. Is it tidal forces from other bodies in the Universe (suns, galaxies, blackholes etc)? Newton's law of motion and all. (In my imagination I see galaxies doing sling shots off each other  crude, I know.) Is it energy from dark matter? I've sometimes thought of dark matter as having a dampening effect on regular matter. 


#17
Apr2411, 06:40 AM

P: 87

Tidal forces from other bodies in the universe act to slow expansion presumably, but not enough to stop it (yet). As bcrowell said, the best current observations and calculations don't allow for the mass of the universe to halt expansion through gravity, and lead to a "crunch". Dark matter is energy, just like matter is energy, and it has no damping effect as far as anyone knows. Dark matter is just a form of matter that doesn't interact with "normal" matter in any way except through gravity, or at a limit that is too small to be measured right now. 


#18
Apr2411, 09:17 AM

P: 219

Thanks again Misericorde.. you have a good way of explaining things.
I guess my "dampening effect" idea came from seeing a science doco which explained how dark matter was first theorized, from observing the outer spirals of some galaxies. In my amateur way I thought of all those stars like ball bearings floating in a lubricant. The "lubricant" helps the bearings flow as well as holds them back from getting too caught up in their own momentum. A bit crude I admit.. lol. 


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