Does the Acceleration of the Universe Change?

[falcon32]

Hi,

I know generically that the expansion rate of the Universe is increasing, hence theoretical dark energy.

But is the acceleration rate itself constant, or does it change? And if it does change, do we have a formula for it yet?

Thanks!

 

[cepheid]

Hello falcon32,

No, the acceleration rate is not constant. Yes, we have an equation that describes how it evolves with time. It's the second one here:

http://en.wikipedia.org/wiki/Friedmann_equations#The_equations

 

[falcon32]

Hello falcon32,

No, the acceleration rate is not constant. Yes, we have an equation that describes how it evolves with time. It's the second one here:

http://en.wikipedia.org/wiki/Friedmann_equations#The_equations

Alright thank you, didn't realize I could wiki it. I've got much to learn...exciting to see the equation that Einstein modified. Did a bit of reading...this equation was created before Hubble discovered the expanding universe, right? So do astronomers still use just this one, or have they made a special one from empirical redshift observations alone?

 

[cepheid]

Alright thank you, didn't realize I could wiki it. I've got much to learn...exciting to see the equation that Einstein modified. Did a bit of reading...this equation was created before Hubble discovered the expanding universe, right? So do astronomers still use just this one, or have they made a special one from empirical redshift observations alone?

Yes, the Friedmann equations are derived from the Einstein Field Equations of General Relativity, and Einstein finished formulating General Relativity in 1915, a few years before Hubble discovered that distant galaxies all appear to be moving away from us.

General Relativity is still the best theory of gravity we have. So, yes, astronomers still use the Friedmann equation in the form given there to this day. However, that is less restrictive than you would think. The Friedman equation doesn't describe a single mathematical model with a single expansion history for the universe, but rather a whole set of models called the "Friedman World Models." The reason for this is that the equations contain certain parameters, and a particular model with a particular expansion rate and history is given by one particular set of values for those parameters. Change the values of the parameters, and you change the outcome predicted by the model. A key task of modern cosmology has been using measurements and observations to figure out which set of parameter values (and hence which world model) accurately describes the universe we live in.

A concrete example may help. One of the main parameters appears in those equations in the form of the density, rho (ρ). A key result of General Relativity is that the geometry of spacetime is affected by its mass-energy content. In the context of the universe as a whole, what this means is that the dynamics of the expansion are affected by the total energy density, ρ, of the universe. This total density rho consists of contributions from all the major constituents: dark energy, dark matter, ordinary matter, and radiation (photons and relativistic particles). There is a separate density parameter for each of these, and we can measure them separately. The total density can be either larger than, equal to, or less than some critical density, ρ_cr. In the classic case (with no dark energy), these three cases lead to the following possibilities:

1. If ρ > ρ_cr, in other words, if there is enough mass in the universe, the universe's expansion slows, stops, and reverses itself, leading to a collapse (the so called "Big Crunch" scenario). You can think of it as there being enough matter in the universe that its mutual gravitation slows down the expansion enough to stop it and reverse it. In this case, there is also positive spatial curvature, meaning that the geometry of the universe is like the geometry on the surface of a sphere.

2. If ρ = ρ_cr, the universe continues to expand forever, albeit at a steadily decreasing rate (there is not enough mass to pull everything back together). In this case, the geometry of the universe is "flat" (meaning that it is Euclidean: it behaves like the geometry you learned in high school). So, at the critical density, there is just enough mass to have no spatial curvature.

3. If ρ < ρ_cr, the universe will also continue to expand forever at a steadily decreasing rate. There will also be negative spatial curvature, meaning that geometry will behave the way it does on the surface of a "saddle."

So, the Friedman equation gives you distinctly different results when you modify the parameters (in this case the total density). Notice that in all three of these scenarios (or "world models"), the universe expands, but that expansion slows down. It turns out that NONE of these three models is right, because in our inventory of the total "mass budget" of the universe, we were missing a major contributor: dark energy. When you throw dark energy into the mix, there is no longer such a straightforward relationship between the mass density of the universe, its geometry (curvature), and its ultimate fate. In the link I sent you, dark energy appears in the form of an additional constant Lambda ($\Lambda$) in the equations. This is the famous "Cosmological Constant." Einstein originally added the cosmological constant because his models predicted that the universe was not static: it could either expand or contract. At the time, this was inconceivable to him. He wanted to make the universe static, so he tried to throw in the extra $\Lambda$ term and tune it to achieve a delicate balance in which the universe neither expanded nor contracted. It turns out that this was futile, because the solutions are unstable. Even if you tune $\Lambda$ to make the universe static NOW, it will not remain so LATER. This was a rookie mistake. If Einstein had stuck to his convictions and followed his own theory to its logical conclusions (the way he did so well when he formulated Special Relativity ten years earlier), he could have predicted the expansion of the universe before Hubble observed it. But Einstein just wasn't thinking outside of the box in this case, and he didn't do that. That's why he later referred to the introduction of the cosmological constant as his "greatest blunder." For a long time, $\Lambda$ fell by the wayside.

Recently (in the mid to late 90's), observations of objects called Type Ia supernovae caused people to bring it back. Type Ia supernovae are thought to result from the thermonuclear explosion of a white dwarf star, and as a result, they are thought to be "standard candles" meaning that they all reach roughly the same peak brightness. So, if you look at how bright one of them appears to be, you can infer its distance. Different Friedman models (with different values for the density parameters) predict different variations of distance (as measured in this way) with redshift. After all, what use is a theoretical model unless if it makes testable predictions? Anyway, by measuring and plotting the Type Ia brightness vs redshift, and finding out which model fits the observed data the best, you can determine the values of the cosmological parameters. In the late 90's, observations of Type Ia supernovae *strongly* favoured a model with a NON-zero value for $\Lambda$. This result has since been corroborated by observations of the Cosmic Microwave Background (CMB). The presence of $\Lambda$ in the equations was attributed to the presence of some as yet unknown and mysterious substance that astronomers termed "dark energy." Dark energy has weird properties. Even though it adds mass to the universe, it also has a repulsive, anti-gravitational effect. So, instead of pulling things together, it forces them apart. So, not only do the observations show that the universe will continue to expand forever, but it also shows that that expansion, rather than slowing down as we thought, will instead get faster and faster and faster with time. This is a crazy result (it won the 2011 Nobel Prize in physics), and it's an example of what you wanted: empirical observations that improve our understanding of the universe. But they do so within the theoretical framework of General Relativity (for now). By the way, the observations also show that the geometry of the universe is very close to being flat (Euclidean): i.e. if you include dark energy, the total density is very close to the critical value.

 

[marcus]

Hi, I started this before supper--didn't see that Cepheid already answered. Then finished post and saw you already have an extensive reply. This is redundant, I guess, but I will let it stand rather than erase.

Falcon you mentioned the *empiricism* issue. My view is that the Friedman equation is good on both empirical AND theoretical counts. Only thing is it is classical---dates from around 1922 before quantum theory was well enough developed to be involved.

That's all right though because we only use Friedman at large scales where Nature behaves classically, so non-quantum equations can be successfully applied.
The Friedman equation has one or two adjustable parameters, the fit is remarkably good. So there is no compelling reason to abandon it. It has another thing going for it: GR as a law of geometry/gravity has been tested in Earth orbit and at solar system scale and at astrophysical scale, it has proven exquisitely accurate, we don't have anything better over a wide range of scale. And Friedman equation has been DERIVED from GR equation. So it agrees with past cosmological observation and has successfully predicted new observations AND it comes out of the best law of gravity we have so far (which itself has been tested every possible way people could think).

So Friedman has outstanding credentials on both empirical and theoretical sides.

The main place it DOESN'T work is right around the start of expansion where the energy density was extreme---and people think that quantum effects on the geometry take over. It is a "classical" (i.e. pre-quantum) equation just like its parent, the 1915 GR equation. So Friedman has not been tested at very small scale and very high energy density. (No more has GR).

That's why people are currently working on versions of GR and of the Friedman equation that incorporate quantum effects on the geometry. Maybe geometry is no longer smooth at very small scale. Maybe a quantum version of GR would not have a "singularity" that is a blow-up point. So they are working on a more rugged version of main GR equation and Friedman equation that will not blow up at the very start of expansion. but which REPRODUCES all the good stuff of the classical equations in the range of conditions where these have been proven to work so well.

That seems to be the next step.

 

[cepheid]

Actually marcus, I think your answer complements mine nicely, hitting on some key points I missed, in spite of my verbosity.

 

[falcon32]

Thanks cepheid and marcus, both of your answers were well-written and thoroughly thought out in my opinion, and I enjoyed reading them. What I love about science is there's always something new to learn: for me, that is about to be trying to understand Einstein's Field Equations. I do understand that GR is the best theory for gravity that we have at the moment, and I would probably shut up if I just had some redshift data that covered a few decades or so that I could play with lol.

 

[Naty1]

The main place it DOESN'T work is right around the start of expansion where the energy density was extreme---and people think that quantum effects on the geometry take over. It is a "classical" (i.e. pre-quantum) equation just like its parent, the 1915 GR equation. So Friedman has not been tested at very small scale and very high energy density.

So here we use INFLATION THEORY pioneered by Alan Guth...just after the Big Bang...something was needed to account for observations such as near flatness...

You might find this discussion worthwhile

How to prove the stretching of space
https://www.physicsforums.com/showthread.php?t=659192&page=2

 

[Mordred]

just to add another reference to the already excellent answers you have recieved, I recently wrote this article on geometry. I'm still trying to figure out how to simplify the FLRW metrics at the 3d and 4d stage. However it should provide some answers.

https://www.physicsforums.com/showpost.php?p=4400002&postcount=1

 

[falcon32]

You might find this discussion worthwhile

How to prove the stretching of space
https://www.physicsforums.com/showthread.php?t=659192&page=2

Thanks for that link, I did find it interesting! Note that my question has never been "is the universe expanding?" but was more along the lines of "did we work backwards from redshift data to arrive at a conclusion?" I appreciate the answers, which were very informative -- it does lead me to the next question though, since it seems the acceleration of the Universe is thought to follow, quite generically a(t)=Ct, rather than a(t)=C...that is, the acceleration increases with time.

1. From your link, we know that the Sachs-Wolf effect slightly blue-shifts photons traveling through gravity wells.
2. We also assume that the Universe is undergoing an accelerating acceleration.
3. Now this takes energy, but this is o.k. since Dark Energy is theorized to perform this work.
4. But the 1st Law of Thermodynamics says that energy cannot be created or destroyed, so we know that we must have a finite amount of Dark Energy to perform the work observed.
5. Therefore, shouldn't we run out of Dark Energy at some point, which would then decelerate a(t) to 0? And if not, does that mean that Dark Matter is converting to Dark Energy along the lines of E=mc²? But that is only delaying the inevitable, since there is a finite amount of Dark Matter available as well.

So to sum it up, while helpful, your link has puzzled me.

 

[Mordred]

Thats the unusual property of dark energy. Its better described as vacuum energy. For the reason you supplied.
the vacuum energy or cosmologucal constant stays consistent in value per m₃. As expansion occurs the total mass energy of the cosmological constant which is positive increases. However the density which is negative pressure stays constant.
The source of energy in regards to the cosmological constant is not fully understood. There are some theories such as virtual particle production. However nothing conclusive.

 

[marcus]

falcon in the most common notation a(t) is the size of a generic distance normalized to a(present)=1 and is called the scalefactor. So watch out there is a potential for confusion when you use a(t) to stand for the acceleration (of what?) there is no definite velocity with which the U expands. One has to pick some distance but there is no agreed on choice.

I guess one quantity that would be proportional to the acceleration of the growth speed of a generic distance would, in conventional cosmo notation, be a"(t) the second derivative of the scalefactor a(t). Just a heads-up about notation that you may be reading sometimes without realizing what is meant. Just in case.

a(t) is a dimensionless quantity, a pure number. So a'(t) is a reciprocal time. The Hubble rate H(t) is defined to be a'(t)/a(t), so it is a reciprocal time. E.g. like 1/144 of one percent per million years.
A number per unit time.

 

[Mordred]

Good to note Marcus.

 

[falcon32]

watch out there is a potential for confusion when you use a(t) to stand for the acceleration (of what?) there is no definite velocity with which the U expands

Alright marcus, thanks for that information, I'll be using better terminology from here on out.

 

[falcon32]

Thats the unusual property of dark energy. Its better described as vacuum energy. For the reason you supplied.
the vacuum energy or cosmologucal constant stays consistent in value per m₃. As expansion occurs the total mass energy of the cosmological constant which is positive increases. However the density which is negative pressure stays constant.
The source of energy in regards to the cosmological constant is not fully understood. There are some theories such as virtual particle production. However nothing conclusive.

Ah ok, so I'm not the only one wondering where the energy is coming from, good to know.
It has been established that the energy, no matter what the ultimate source, is finite, correct?

 

[Mordred]

Ah ok, so I'm not the only one wondering where the energy is coming from, good to know.
It has been established that the energy, no matter what the ultimate source, is finite, correct?

Personally in regards to the term "source" in this case I prefer "property".

I would have to answer no in the case total lamnda. For one we don't know if the universe is finite. In terms of density then yes its a finite amount. Also the total amount of DE will continue for as long as the universe continues to expand. Pressure due to DE will stay the same.

If your not aware the energy density and pressure per volume
are equivelent terms in units. You probably are, however saying so supplies that info for others reading this good info thread

 

[falcon32]

Personally in regards to the term "source" in this case I prefer "property".

I would have to answer no in the case total lamnda. For one we don't know if the universe is finite. In terms of density then yes its a finite amount. Also the total amount of DE will continue for as long as the universe continues to expand. Pressure due to DE will stay the same.

If your not aware the energy density and pressure per volume
are equivelent terms in units. You probably are, however saying so supplies that info for others reading this good info thread

The missing wide-angle correlations in the CMB are good support for a finite Universe, so say many.

 

[Mordred]

Yes I agree good support however that's not the same as conclusive.

 

[Naty1]

generically a(t)=Ct, rather than a(t)=C...that is, the acceleration increases with time.

not sure what you have in mind here...since about 7B years the acceleration has been increasing...as we leave a matter dominated era [mass closer together] and enter a radiation dominated era [mass, like galaxies, more widely separated].

For an introduction to expansion concepts, try Leonard Susskind Cosmology lecture #3, Youtube, the first 20 minutes or so...He derives, using simply concepts and math, expansion measures. It's a recap. If you want the full very slow and deliberate version watch Lecture #2.

2. We also assume that the Universe is undergoing an accelerating acceleration.

yes, based on observations, we seem to have evidence...like Hubble's observations

3. Now this takes energy, but this is o.k. since Dark Energy is theorized to perform this work.

That idea has come into come recent question. When the cosmological constant is associatred with dark energy, whether expansion requires energy, I don't believe is resolved one way or the other.

4. But the 1st Law of Thermodynamics says that energy cannot be created or destroyed, so we know that we must have a finite amount of Dark Energy to perform the work observed.

Conservation of energy does not apply to cosmology...that is, it is undefined for curved spacetime...

5. Therefore, shouldn't we run out of Dark Energy at some point, which would then decelerate a(t) to 0? And if not, does that mean that Dark Matter is converting to Dark Energy along the lines of E=mc2? But that is only delaying the inevitable, since there is a finite amount of Dark Matter available as well.

So far the consensus is that expansion will continue. It's been going for 13.8 B years and is NOT 'running out of steam'...no evidence that energy for expansion, if that is in fact present, is going to be in short supply. As Susskind's lecture shows, one expansion gets started it seems to keep going...and, yes, that sure seems strange.

So to sum it up, while helpful, your link has puzzled me.

Good. There is much to be puzzled about!Much we have yet to understand.

 

[falcon32]

For an introduction to expansion concepts, try Leonard Susskind Cosmology lecture #3, Youtube, the first 20 minutes or so...He derives, using simply concepts and math, expansion measures. It's a recap. If you want the full very slow and deliberate version watch Lecture #2.
...
That idea has come into come recent question. When the cosmological constant is associatred with dark energy, whether expansion requires energy, I don't believe is resolved one way or the other.

Thanks for the link Naty1, I am definitely watching the lecture, its probable I'm confused because I don't have the basics down for expansion yet. By the way, you seemed to contradict yourself in that last sentence. If expansion does not require energy, then why did astrophysicists introduce it in the first place upon noticing the acceleration? Why add something frivolous?

Conservation of energy does not apply to cosmology...that is, it is undefined for curved spacetime...

This is a bit much, I am expected to understand that the 1st Law holds true in regions like our galaxy, and yet, does not hold true on a Universe scale?

Good. There is much to be puzzled about!Much we have yet to understand.

Heartily agree.

 

[Naty1]

If expansion does not require energy, then why did astrophysicists introduce it in the first place upon noticing the acceleration?

It seemed like a good idea at the time! Keep in mind the cosmological constant, λ, is a constant term that results from integration...like those "C's " you might have used when integrating.

What λ actual represents remains an open issue, I think...

I am expected to understand that the 1st Law holds true in regions like our galaxy, and yet, does not hold true on a Universe scale?

probably. The essential difference is that a galaxy is really a 'local region' that is not expanding; you can't say that about the entire universe which IS expanding.

In a space-time that is neither stationary nor asymptotically flat, such as in the FRW space-times used to describe our expanding universe, there is no good way to define a conserved "total energy".

In another discussion Chronos had this to say:

In GR, there is not even an unambiguous definition for global energy, so, it is rather difficult to address conserving that which is undefined. Current theory suggests the total energy of the universe was fixed by the time the inflationary epoch ended. Kinetic energy [change] due to expansion is an illusion. All galaxies have a fixed amount of kinetic energy within their own local reference frame.

 

[falcon32]

It seemed like a good idea at the time! Keep in mind the cosmological constant, λ, is a constant term that results from integration...like those "C's " you might have used when integrating.

What λ actual represents remains an open issue, I think...

You may be right, Naty1. Perhaps λ does not represent Dark Energy. But my point is that you cannot argue that extra energy has not been added to the universe. In the Integrated Sachs-Wolf effect, we clearly see a photon blueshifted...quite literally, energy has been added to it.
In a previous post I had seen Dark Energy held responsible for this, which would make sense, and vindicate the formulation of the concept of D.E. But regardless of what you ultimately blame, the photon was blueshifted, and the extra energy had to come from somewhere.

(I found this an interesting read http://preposterousuniverse.com/teaching/371/papers06/sherman-371.pdf)

 

[Mordred]

Ok let me put it to you this way.
DE is a negative pressure scalar value. Pressure has energy potental in the form of kinetic energy. Take a closed pressure system such as a piston. with pressure P. Open up the piston to increase the volume. The pressure stays the same. In order for that to occur energy must be supplied. In the case of the cylinder its supplied by the mechanical energy of pulling on the piston

in expansion its supplied via quantum fields. As one proposal or rather their are several QM proposals for that mechanism.
The key point is its easier to relate to if you treat DE more in terms of pressure. As I mentioned before pressure and density are equivelent

 

[falcon32]

Ok let me put it to you this way.
DE is a negative pressure scalar value. Pressure has energy potental in the form of kinetic energy. Take a closed pressure system such as a piston. with pressure P. Open up the piston to increase the volume. The pressure stays the same. In order for that to occur energy must be supplied. In the case of the cylinder its supplied by the mechanical energy of pulling on the piston

in expansion its supplied via quantum fields. As one proposal or rather their are several QM proposals for that mechanism.
The key point is its easier to relate to if you treat DE more in terms of pressure. As I mentioned before pressure and density are equivelent

O.K., in your analogy we have a perfect cylinder (no ring leakage) which is closed, meaning the air inside is trapped, so that we can compress or rarefy it at will. We open it up, meaning we pull on the piston to increase the volume of the cylinder. But this of course creates a vacuum -- and this vacuum is what I believe you're terming DE? A "negative pressure scalar value" you said (note that the energy of the piston's movement went into creating the vacuum, not raising the pressure of the gas inside).
At any rate, in order for pressure inside the new volume of the cylinder to equal the old pressure, we must add energy into the system. This would be what I would term DE, but if I'm understanding your analogy, quantum fields come into play here, acting as the conduit to supply DE.

Or did you just mean moving a piston within a cylinder that is open to the air, so that it can intake? In that case you are correct, the pressure inside the piston would be constant. But this by definition would not be a closed system, since now we are interacting with the piston's environment.

 

[Mordred]

Thats correct, by the way that analogy is used to describe false vacuum by A.Guth. Inside the piston is false vacuum. (lowest energy density state). the region outside is the true vacuum. The piston walls and gasket is the barrier,(higgs field). quantum tunneling occurs from false vacuum and true vacuum.
this model is "old inflation" there are numerous later inflation proposals as well as expansion proposals. Many of them use diferrent quantum fields such as the inflaton. Parkers radiation. Slow roll approximation, higgs field itself
natural inflation etc. There is over 100 of them lol. Granted some of those mentioned deal with inflation specifically but they help understand expansion in so far as examples of how energy may be supplied ie Dark energy to maintain the same pressure

 

[Naty1]

"But my point is that you cannot argue that extra energy has not been added to the universe."

Of course I can...that is incorrect.

"... In the Integrated Sachs-Wolf effect, we clearly see a photon blueshifted...quite literally, energy has been added to it.''"

You mean the frame of observation has changed slightly.

Why not think about 'the energy that has been added' in one entity as coming from cooling of
the universe as it expands?

But of course all this is rather incomplete reasoning...Where did all "the energy that has been added" to the recent Oklahoma tornadoes come from?? Do you think there was energy added to Earth's atmosphere??

 

[Mordred]

You mean the frame of observation has changed slightly.

Why not think about 'the energy that has been added' as coming from cooling of
the universe as it expands?

thats backwards Naty cooling occurs as a result of expansion not as a cause of expansion

 

[Naty1]

cooling occurs as a result of expansion not as a cause of expansion

that's what I posted. one entity loses a bit of energy..another gains a bit...

 

[Mordred]

Sorry I misread that statement

 

[marcus]

...

1. From your link, we know that the Sachs-Wolf effect slightly blue-shifts photons traveling through gravity wells.
2. We also assume that the Universe is undergoing an accelerating acceleration.
3. Now this takes energy, but this is o.k. since Dark Energy is theorized to perform this work.
4. But the 1st Law of Thermodynamics says that energy cannot be created or destroyed, so we know that we must have a finite amount of Dark Energy to perform the work observed.
5. Therefore, shouldn't we run out of Dark Energy at some point, which would then decelerate a(t) to 0? And if not, does that mean that Dark Matter is converting to Dark Energy along the lines of E=mc²? But that is only delaying the inevitable, since there is a finite amount of Dark Matter available as well.

So to sum it up, while helpful, your link has puzzled me.

Watch out. The 1st law is believed to hold in static geometry (approximately what we have at local scale---the scale say of our local group of galaxies)
It has not been shown to hold in an expanding geometry. But in a very slightly expanding geometry it nearly holds, so we can use it---as long as the error is negligible.

sean carroll has a long blog piece on this titled "energy is not conserved in an expanding universe". He is a reputable guy--many people use his textbook on GR and he gets invited to give talks all over the place. I don't necessarily like him, but he is a smart Caltech guy and a very good communicator.

It is a well known fact that energy is not conserved in a dynamic geometry situation. John Baez also has an essay explaining this. He is another prominent math-physics explainer. I like him a lot, but I think in this case Sean Carroll's essay is clear and forceful. Maybe you should google it. The title and the name should do it, say "carroll energy not conserved expanding" or something.

Expansion would be going on even if there were no "dark energy". It looks like the cosmological curvature constant may simply be a constant of nature, like Newton's constant G. It occurs naturally in the Einstein equation of GR and we had no right to assume that it was zero. As such it is not "used up" any more than the Newton G constant is "used up". There is a lot of hype and BS about this, but it has been dying down recently. Cosmologists are more apt to refer to the cosmo constant, and not say "dark energy" when they are writing for each other, than they were, say 5 or 10 years ago. More stimulating language is customarily used when writing for the public.

Google "rovelli prejudices constant" for a 2010 article debunking the "dark energy" buzzword business. Of course you CAN imagine the curvature constant to be caused by some mysterious "energy" field, but there is no evidence that it actually is. A lot of people like to think of it that way. but also a lot of people prefer to think of the cosmological curvature constant is simply that, a constant of nature like the other physical constants.

Dark MATTER on the other hand clumps and clusters like other matter and we can see it by its lensing effect on the galaxies behind it, its gravity bends light. there is a whole bunch of many kinds of solid evidence for DM and people actually make density contour maps of DM clouds. So that is a totally different issue from "dark energy". It's all fun

If you try googling and the titles don't work, tell me and I'll get the links to the carroll and rovelli articles.

 

[falcon32]

"But my point is that you cannot argue that extra energy has not been added to the universe."

Of course I can...that is incorrect.

"... In the Integrated Sachs-Wolf effect, we clearly see a photon blueshifted...quite literally, energy has been added to it.''"

You mean the frame of observation has changed slightly.

Why not think about 'the energy that has been added' in one entity as coming from cooling of
the universe as it expands?

But of course all this is rather incomplete reasoning...Where did all "the energy that has been added" to the recent Oklahoma tornadoes come from?? Do you think there was energy added to Earth's atmosphere??

I might have phrased my last post a little too succinctly. Now not to be facetious, but do I think energy is being added to Earth's atmosphere? Every day the Sun shines (those 1400 watts/m² come in handy now and then)!

Hmm, thinking of a blueshifted photon as cooling from the Universe's expansion is good alternative way to look at this situation -- thanks! However, this would demand that it takes energy to expand the Universe...something I find quite natural, since it is accelerating against gravity, but something that others do not like for their own reasons.

But I still think this is a bit of a paradox.
Suppose you have three experimenters, all with watches that have been synchronized. Experimenter A stays in our Milky Way galaxy, the other two, B and C -- having identical scientific equipment -- travel out to the Andromeda galaxy, and position themselves at the base points of an isosceles triangle, with A being at the apex. The triangle base is wide enough so that B is very far away from Andromeda, and therefore any gravitational effect on photons he shines will be negligible.
But C's triangle leg passes just to the right of Andromeda's black hole (from A's perspective), so that it experiences the maximum gravitational effect (note that any photons C shines will undergo gravitational lensing, and therefore, from his perspective, he must aim a little to his left in order to hit A; likewise B must back up just a bit so that the two paths are still of equal length. So the total geometry closely approximates a triangle, but is not).
Now then, at a predetermined time, both B and C fire light beams at A. Both will travel exactly the same distance. However, the Sachs-Wolf effect will very slightly blueshift C's photons. B's will remain unaffected.
Now since both light beams were created with exactly the same apparatus, and traveled exactly the same distance, why does one have more energy than the other?

 

[falcon32]

Awesome marcus, looking into the links and thanks

 

[marcus]

Falcon, if you are interested in acceleration of the geometric expansion process maybe you should learn (very easy and quick) ability to make charts of it with the standard cosmic model. Try this:
open http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html
click "set sample chart range"
click "column definition and selection" which gives a menu and deselect everything but Time, Hubble radius, Distance_then, and "a' R_0".
This last thing is actually the EXPANSION SPEED OF A SAMPLE DISTANCE plotted over time, so you can see it decline at first, until around year 7 billion, and then gradually build up. Acceleration is not very dramatic so the build-up is not very dramatic but at least you can get a handle on it.

Then press "calculate". That will give a table with four columns: Time, Hubble radius, Distance of past lightcone at that time, and growth speed of the sample distance (as a multiple of the speed of light)

Then if you go back and click on the "chart" button and AGAIN press "calculate" you will get a chart with blue, red, and gold curves plotted over time.

blue is Hubble radius (the size of distance that is expanding at speed c)
red is D_then, the distance to a photon which is coming towards us and will get here today (but then continues on into future, away from us)
gold is the expansion speed of a sample distance (the chosen distance is one which for definiteness is equal to the Hubble radius 14.4 billion ly at present, you have to pick some distance to have a definite speed since the speed depends on the size of distance).

When you have the "column selection" menu open you mostly just UNCHECK the items you don't want which happen to be checked as the DEFAULT.
So you uncheck "scale factor" for example. Another time you might want it and leave it checked.
BUT THE sample speed item labeled "a'R_0" you actually have to CHECK because it is not part of the default and will not appear unless you explicitly indicate you want it.
I think if you do actually open the "column" menu you will see what I mean. Checking that is what will get you the gold curve plotted.
It is not all that dramatic, as I say, but it does show how the growth speed of a generic distance changes over time, and the minimum speed around year 7 billion.
All distances have the same speed profile shape, just proportioned to their size.

 

[Naty1]

Now not to be facetious, but do I think energy is being added to Earth's atmosphere? Every day the Sun shines (those 1400 watts/m2 come in handy now and then)!

And every day it radiates away that energy...well, sometimes a bit more, sometimes a bit less...the former are cooling periods the latter warming periods...

talk about facetious...just don't leave this discussion thinking that I have said the heat lost with cosmological expansion powers the Sachs Wolfe...I have no idea about all those very complicated relationships...for all we know maybe there is a some gain or loss of energy...I
don' t think we have observational evidence one way or the other...

 

[Mordred]

You may find this article on Sach-Wolfe effect of interest.

http://arxiv.org/abs/0801.4380

though on the technical side there is some good information within it