Expansion of the Universe question

[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.

 

[bcrowell]

Current observations show that the expansion is accelerating.

 

[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 into 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.

 

[Angry Citizen]

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

 

[phinds]

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)
I hope someone can clear this up for me.

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.

 

[Drakkith]

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.

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

 

[marcus]

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

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.

 

[Angry Citizen]

I may be missing something here but you seem to be saying that if the acceleration becomes a constant, then so would the velocity.

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.

 

[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.

 

[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.

 

[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/spiface/find/hep/www?rawcmd=FIND+%28DK+QUANTUM+GRAVITY%2C+LOOP+SPACE+OR+DK+QUANTUM+COSMOLOGY%2C+LOOP+SPACE%29+AND+%28DK+PRIMORDIAL%2C+FLUCTUATION+OR+DK+INFLATION+OR+DK+COSMIC+BACKGROUND+RADIATION%29+AND+DATE+%3E+2007&FORMAT=www&SEQUENCE=citecount%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.

 

[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 don't 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.

Thanks for you reply.

 

[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.

 

[Cosmo Novice]

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.

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

 

[bcrowell]

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.

Your information is a little out of date here.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

 

[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.

 

[Misericorde]

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.

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.

 

[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.

 

[phinds]

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.

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.

 

[bcrowell]

One thing I've missed in this is: What is fueling the acceleration?

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.

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.

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

What is fueling this expansion, nobody knows, but there are guesses.

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

Maybe it's the old concept of a potential energy curve into a plateau from initial inflation,[...]

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

[...]or maybe it's vacuum expectation energy.

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.

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".

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

 

[narrator]

Thanks bcrowel... my appetite is growing..
a bit like the French saying, l'appetit viens en mangant - appetite comes by eating

 

[phinds]

Originally Posted by 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".

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


Yes, I quite agree and in fact, If you'll reread my statement, you'll see that I didn't say that dark energy causes the expansion, I said it causes the acceleration.

 

[bcrowell]

Yes, I quite agree and in fact, If you'll reread my statement, you'll see that I didn't say that dark energy causes the expansion, I said it causes the acceleration.

Oops, sorry. I didn't read your post carefully enough.

 

[cepheid]

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.

Well, maybe you already know all of this, but the Friedmann equation can just be written as

$$\left(\frac{\dot{a}}{a}\right)^2 = \frac{8 \pi G}{3}\rho_{\textrm{tot}}$$​

where a is the scale factor and $\rho_{\textrm{tot}}$ is the total energy density of the universe. Now, assuming that $\rho_{\textrm{tot}} = \rho_m + \rho_{\textrm{de}}$, i.e. matter and dark energy are the two important components, then we have:

$$\left(\frac{\dot{a}}{a}\right)^2 = \frac{8 \pi G}{3}\rho_{m} + \frac{8 \pi G}{3}\rho_{\textrm{de}}$$​

Now, the interesting part is the relation that determines how the density of a component varies with scale factor. It's just given by:

$$\frac{d\rho}{da} +\frac{3}{a}(\rho + P) = 0$$​

I think that the proper way to derive this is from the condition in general relativity that the covariant derivative of the stress-energy tensor vanishes. However, you can derive it from simple thermodynamic arguments. Just consider that any given volume in the universe expands adiabatically (no heat transfer in or out) so that the 1st law of thermodynamics says dU = -PdV where U is the total internal energy in that volume. Then you just consider that V ~ a³ and you can get the equation above. Now, consider the equation of state (the relationship between pressure and density) for a given constituent of the universe:

$$P = w\rho$$​

Non-relativistic matter is essentially pressure-less so that w_m = 0. Plugging that into the equation above gives you:

$$\frac{d}{da}(\rho_m a^3) = 0~~~~\Rightarrow \rho_m a^3 = \textrm{const.}~~~~\Rightarrow \rho_m \propto a^{-3}$$​

Now, for a generic component where we may not be entirely sure what w is, solving the equation gives you:

$$\rho a^{3(1+w)} = \textrm{const.}$$​

So, the evolution of the energy density of dark energy with scale factor depends on the equation of state of dark energy i.e. it depends on w_de, which I'll just call w from now on. You can see that if w = -1 (which we think it is close to), we just end up with the result that:

$$\rho_{\textrm{de}} = \textrm{const.}$$​

If that's true, then I can write my Friedmann equation above as:

$$\left(\frac{\dot{a}}{a}\right)^2 = \frac{8 \pi G}{3}\rho_{m} + \frac{\Lambda}{3}$$​

where

$$\Lambda \equiv 8 \pi G \rho_{\textrm{de}}$$​

is a constant. That leads me to the whole point of my post, which was to address marcus' quoted statement above by explaining that for dark energy, w = -1 is consistent with a cosmological constant $\Lambda$.

If w is not exactly equal to -1, then you have some other more exotic form of dark energy that cannot be expressed as a cosmological constant term in the Friedmann equation. But you could still express that equation in terms of the parameter w and other constants. To do this, we need two facts. One is that the density parameter $\Omega_i$ for the i^th constituent of the universe is defined as $\rho_{i,0}/\rho_{\textrm{cr}}$ where the zero in the subscript denotes the value of the density today, and the reciprocal of the critical density is just $8 \pi G / 3H_0^2$. Using these relations, the Friedmann equation becomes:

$$\left(\frac{\dot{a}}{a}\right)^2 = \frac{8 \pi G}{3}(\rho_{m,0})a^{-3} + \frac{8 \pi G}{3}(\rho_{\textrm{de,0}})a^{-3(1+w)}$$

$$\left(\frac{\dot{a}}{a}\right)^2 = H_0^2\left(\frac{\rho_{m,0}}{\rho_{\textrm{cr}}} \right)a^{-3}+ H_0^2\left(\frac{\rho_{\textrm{de,0}}}{\rho_{\text{cr}}}\right)a^{-3(1+w)} $$


$$\left(\frac{\dot{a}}{a}\right)^2 = H_0^2\Omega_m a^{-3} + H_0^2\Omega_{\textrm{de}} a^{-3(1+w)}$$​

Since the left-hand side is just the the square of Hubble parameter H, it's nice to express the final result as

$$H^2 = H_0^2[\Omega_m a^{-3} + \Omega_{\textrm{de}} a^{-3(1+w)}]$$​

So you do need to explicitly include w in the case where it is not -1 and the effect of dark energy cannot be expressed as a cosmological constant term in the equations. I'm not sure whether any of this adds to the discussion, but I thought it was good to include for completeness. I've omitted the curvature term in the Friedmann equations throughout this discussion, so I guess I've implicitly assumed a flat universe.

 

[Misericorde]

Sorry bcrowell, I guess I did mix up my concepts quite a lot. Thanks for the detailed response, and not letting it slide.

 

[marcus]

Hey Cepheid, post #24 is a beautiful piece of work!
Mathematically neat, economical.
Clear expository style.
Notation and visual layout perfect.

Did anybody else notice this? Anybody see any flaw that needs fixing? I don't, but I'm not the greatest proofreader.

I'll try to get some staff attention to see if they can use stuff like this in PF's library of explanations/FAQ-type thing.

 

[MEMoirist]

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.

I suspect that by extending your question beyond the above, you take the question too far and cause yourself confusion. When you go beyond the above mathematically certain end of the known universe, you return to the initial question of what caused the universe to expand in the first place. Given that the universe will have become irrelevant, anything beyond the above isn't a logical question.

Logic dictates that the next question is, "Does life continue after physical death".

If sentient energy created the universe as a dream, then at death, the whole and the parts, right down to the smallest particle, simply wake up as the intelligent energy that they are. Energy can never be destroyed. The universe will have been made irrelevant, unless the intelligent energy learns from it. If it learns from it, it will not have been an irrelevant event.

 

[Misericorde]

I suspect that by extending your question beyond the above, you take the question too far and cause yourself confusion. When you go beyond the above mathematically certain end of the known universe, you return to the initial question of what caused the universe to expand in the first place. Given that the universe will have become irrelevant, anything beyond the above isn't a logical question.

Logic dictates that the next question is, "Does life continue after physical death".

If sentient energy created the universe as a dream, then at death, the whole and the parts, right down to the smallest particle, simply wake up as the intelligent energy that they are. Energy can never be destroyed. The universe will have been made irrelevant, unless the intelligent energy learns from it. If it learns from it, it will not have been an irrelevant event.

What on Earth are you talking about, and what does it have to do with universal expansion? It sounds as though you're just talking about your idea of God, nothing more, and that is hardly relevant here even if you believe in God.

 

[phinds]

What on Earth are you talking about, and what does it have to do with universal expansion? It sounds as though you're just talking about your idea of God, nothing more, and that is hardly relevant here even if you believe in God.

I agree w/ this statement.

 

[MEMoirist]

What I tried to say is that once you have reached the point where the universe has expanded itself so much that it has become irrelevant, you have reached the limit of that conversation on that level. There is no further you can take it and still make sense.

I thought that my quoting the post that I was replying too, that much at least would be evident.

From the point where the universe has basically expanded itself out of existence, you can only look for a way to make it "have been" relevant" in the past tense. Tiime and Space will no longer provide a medium. But the questioner was making it hard for himself by trying to go beyond the limits of time and space, beyond the limits of science. As I recall, he wanted to go describe what comes after.

By seeing the world reach irrelevancy, he has brought the question back to the question of what started the universe, which, I recall, is what I said.

It wasn't MY religion that I posed as an example of the only type of direction left for thought after relevance. It wasn't my intent to discuss religion on a science forum, which is why the idea was so bizarre. But if a thought process (applying science to nothing) is leading nowhere, wouldn't you like to know it before you went too far with it?

If it wasn't your quote that I used in the post, and I did remain on-topic, why are you offended? Do you disagree? Can you take science beyond the end of the universe's relevance? Can science describe that which doesn't exist?

 

[narrator]

If it wasn't your quote that I used in the post, and I did remain on-topic, why are you offended? Do you disagree? Can you take science beyond the end of the universe's relevance? Can science describe that which doesn't exist?

From what I've read and seen on doco's, in the dying phase of the universe, it will just go dark and have a lot of lumps of cold rock floating at great distance from each other (far greater than they are now). Thus it endeth. What else is there to say? (Except that there's still the recycle theory.. lol)

If there is a deity responsible for it all, then we have as much chance of attributing anything to it as an ant would of understanding cosmology. Until that deity changes its policy of non-disclosure, science will never discover it. Thus, this forum is about what science HAS uncovered, and not about speculations outside its charter. (Have I got that right, mods?)

I do contemplate such questions, but not while I'm posting here.

 

[CutterMcCool]

@Marcus,

Thanks for your thorough answers. If space is expanding exponentially, shouldn't it be possible to follow the "leading edge" of space (the outer edge of the observable universe) and describe its acceleration in m/s^2? Much as the gravitational acceleration of a falling body on Earth (about 9.8 m/s^2) is expressed in that form? Which says its velocity would be increasing while its acceleration rate is constant.

Also in the Friedmann equations you mention, what is p and a'?

 

[marcus]

I hope someone else will help answer, McCool. I got distracted elsewhere and didn't see your question. Did you look up the Friedmann eqns. on wikipedia? Let us know what online thing you are looking at, give a link, so we can see what you see.

Typically in those equations, a(t) is a handle on distances called scalefactor, and a-dot or a-prime is the time derivative. a'(t) = da/dt.
Do you know some elementary calculus so that the notation da/dt means something. It is the increase per unit time.

The scalefactor a(t) is normalized so that it equals 1 in the present. So if you go back in time to some time when distances were just half as big then a(t) would = 0.5.
And if you go to some time in future when distances are three times as big then a(t) would = 3.

the Friedmann eqn usually has a greek letter rho in it which stands for the density. The grams per unit volume---in whatever units.

RHO LOOKS LIKE A LETTER P
which is confusing, sorry about that. And also one of the equations you often see together with the main one has an actual letter p, standing for pressure.

If there is something in the U that exerts a pressure that could also have an effect.

Most often though when you see something vaguely like a lowercase letter p it is actually rho, the density.

If you've had even a bit of calculus it's a lot easier to understand, so I hope you will let us know that you have. And then others may help explain the friedmann equations. they are pretty basic actually.

Did you ever visit Ned Wright's cosmology tutorial website?
if not google "ned wright"
and "wright balloon model"
and "wright cosmo calculator"
He has an FAQ
He has lots of diagrams showing the observable U, and the past lightcone, etc. How expansion affects the shape of things.

Let us know if you find anything especially good online stuff on your own. Share the goodies

 

[cepheid]

@Marcus,

Thanks for your thorough answers. If space is expanding exponentially, shouldn't it be possible to follow the "leading edge" of space (the outer edge of the observable universe) and describe its acceleration in m/s^2? Much as the gravitational acceleration of a falling body on Earth (about 9.8 m/s^2) is expressed in that form? Which says its velocity would be increasing while its acceleration rate is constant.

I hope someone else will help answer, McCool. I got distracted elsewhere and didn't see your question. Did you look up the Friedmann eqns. on wikipedia? Let us know what online thing you are looking at, give a link, so we can see what you see.

Hey marcus,

It occurred to me a few days ago that it should be possible to do what CutterMcCool is proposing by simply twice-differentiating the expression for the horizon radius as a function of time (the second equation here: http://en.wikipedia.org/wiki/Observable_universe#Particle_horizon)

Differentiating it once (assuming I did it right) leads to a neat result, in the sense that I think it has a ready interpretation. I use x for co-moving distance and r for physical distance, and I use the subscript H to mean, "horizon." The co-moving horizon x_H is the same as eta in that link, except that I explicitly include a factor of c in front of the integral. Then we get (using a ' symbol to mean differentiation w.r.t. proper time):

r'_H(t) = [a(t)x_H(t)]' = a'x_H + ax'_H

But ax'_H just equals c (since if you differentiate that integral, you just end up with the function in the integrand, 1/a, and ac/a = c). That leaves us with:

r'_H = a'x_H + c

So it seems that the radius of our observable universe (namely r_H) is getting bigger for two reasons. The first reason, associated with the first term above, is that everything in the current
horizon volume is getting bigger due to expansion, and this just occurs at a rate a'. The second reason is that the horizon volume itself is expanding to encompass more stuff that was not contained within it before. This just occurs at rate c, as more photons reach us! This second reason can be thought of as an expansion of the co-moving horizon volume, which is why it is associated with the second (x') term.

What do you think of my interpretation? If it's correct then, it is pretty neat. So, if you wanted to, you could think of this quantity a'x_H + c as the velocity with which the horizon boundary recedes from us in m/s.

To get the acceleration, we just differentiate again, giving us:

r''_H = a''x_H + a'x'_H

I have no ready interpretation for this!

 

[jbwright]

by The Angry Citizen:

I hope you all (4/8/11 to 4/30/11) won't get too angry when you discover that Creation (of something to go "bang", necessary for a Big Bang) requires an act of magic and that magic is not allowed when one studies the Universe. Instead, you must recognize objective reality as your tool in this epistemological arena.

The Cosmological Redshift? How else could it be developed? Try studying the Galactic Clusters that thoroughly dominate our Universe, and observe that redshifts (a side show) are like light light from a forest fire. And see where else a Galactic Cluster will lead you.