# Expansion of the Universe question

1. Apr 7, 2011

### Angry Citizen

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. Apr 7, 2011

### bcrowell

Staff Emeritus
Current observations show that the expansion is accelerating.

3. Apr 7, 2011

### marcus

Cosmologists don't have certainties. All they can do is fit model to data---find 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 best-fit 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.

Last edited: Apr 7, 2011
4. Apr 7, 2011

### Angry Citizen

Thank you, that's just what I wanted to know!

5. Apr 22, 2011

### phinds

I may be missing something here but you seem to be saying that if the acceleration becomes a constant, then so would the velocity. That is mathematically nonsensical unless the constant (for the acceleration) is zero, but I take "static" to mean a non-zero constant. Again, I may be misinterpreting what you are saying.

6. Apr 22, 2011

### Staff: Mentor

I think they mean that there might be a time where the acceleration stops increasing and becomes a set acceleration before starting to decrease.

7. Apr 22, 2011

### marcus

Drakkith, it is so much easier to use math functions like a(t).
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 values---closely 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.

Last edited: Apr 22, 2011
8. Apr 22, 2011

### Angry Citizen

Pardon, I meant that if acceleration was changing negatively (IE decreasing over time), then eventually it would reach a point where acceleration was zero -- constant velocity. It would then begin to have a negative acceleration. However, a'' doesn't seem to be changing at all, judging by the information in this thread.

9. Apr 22, 2011

### marcus

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 well-defined 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 indefinitely---a 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 interest----exponential growth---something 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.

Last edited: Apr 22, 2011
10. Apr 22, 2011

### Cosmo Novice

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. Apr 22, 2011

### marcus

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 non-expert 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 fit---the 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 pre-bang.

I recently did a search at the (German mirror of) Stanford-SLAC 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://www-library.desy.de/cgi-bin/...+DATE+>+2007&FORMAT=www&SEQUENCE=citecount(d)

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.

Last edited: Apr 22, 2011
12. Apr 22, 2011

### Cosmo Novice

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 U-3,U-2,U-1,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.

13. Apr 22, 2011

### AstrophysicsX

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. Apr 22, 2011

### Cosmo Novice

That sounds as if you are categorically stating that U is finite, because if U is infinite and therefore homogeneous, then the further you get from a given point, the faster recession becomes, given an infinite U this would imply infinite expansion.

Or am I missing your point?

Thanks

15. Apr 23, 2011

### bcrowell

Staff Emeritus
Your information is a little out of date here. Models with a "Big Crunch" are now ruled out by both supernova and CMB observations.

16. Apr 24, 2011

### narrator

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, black-holes 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. Apr 24, 2011

### Misericorde

What is fueling this expansion, nobody knows, but there are guesses. Maybe it's the old concept of a potential energy curve into a plateau from initial inflation, or maybe it's vacuum expectation energy.

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. Apr 24, 2011

### narrator

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.

19. Apr 24, 2011

### phinds

There is a force, or SOMETHING, that creates the acceleration. No one has a clue what it is or how it works. To avoid having to say those two sentences every time we want to talk about, a shorthad has been created that means the same thing as those two sentences. The shorthand is "dark energy".

As Misericorde said, dark matter (another shorthand phrase meaning "we don't know what the ... ") IS matter. It pulls the U inward but is overcome, along with regular matter, by dark energy.

I think speculation about dark matter is farther along than speculation about dark energy, but that's more a belief on my part than anything I could substantiate from my limited knowledge so if I'm wrong, I'm sure someone more knowledgeable will jump in.

20. Apr 24, 2011

### bcrowell

Staff Emeritus
The Newtonian analogy can be misleading, but there is an element of truth to it here. In the Newtonian analogy it's just running on inertia.

Energy is not conserved in cosmology. See the FAQ entry below.

No, there is no mystery. This is all well understood in the framework of general relativity.

Inflation isn't relevant to understanding why the universe is currently expanding.

This would be relevant to explaining why the cosmological constant has the value it does, which *is* a mystery. But you don't need the cosmological constant to understand why the universe is expanding, only to understand why the expansion is currently accelerating.

Again, this is only relevant to explaining why the expansion is *accelerating*.

FAQ: How does conservation of energy work in general relativity, and how does this apply to cosmology? What is the total mass-energy of the universe?

Conservation of energy doesn't apply to cosmology. General relativity doesn't have a conserved scalar mass-energy that can be defined in all spacetimes.[MTW] There is no standard way to define the total energy of the universe (regardless of whether the universe is spatially finite or infinite). There is not even any standard way to define the total mass-energy of the *observable* universe. There is no standard way to say whether or not mass-energy is conserved during cosmological expansion.

Note the repeated use of the word "standard" above. To amplify further on this point, there is a variety of possible ways to define mass-energy in general relativity. Some of these (Komar mass, ADM mass [Wald, p. 293], Bondi mass [Wald, p. 291]) are valid tensors, while others are things known as "pseudo-tensors" [Berman 1981]. Pseudo-tensors have various undesirable properties, such as coordinate-dependence.[Weiss] The tensorial definitions only apply to spacetimes that have certain special properties, such as asymptotic flatness or stationarity, and cosmological spacetimes don't have those properties. For certain pseudo-tensor definitions of mass-energy, the total energy of a closed universe can be calculated, and is zero.[Berman 2009] This does not mean that "the" energy of the universe is zero, especially since our universe is not closed.

One can also estimate certain quantities such as the sum of the rest masses of all the hydrogen atoms in the observable universe, which is something like 10^54 kg. Such an estimate is not the same thing as the total mass-energy of the observable universe (which can't even be defined). It is not the mass-energy measured by any observer in any particular state of motion, and it is not conserved.

MTW: Misner, Thorne, and Wheeler, Gravitation, 1973. See p. 457.

Berman 1981: M. Berman, unpublished M.Sc. thesis, 1981.

Berman 2009: M. Berman, Int J Theor Phys, http://www.springerlink.com/content/357757q4g88144p0/

Weiss and Baez, "Is Energy Conserved in General Relativity?," http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

Wald, General Relativity, 1984