Is accelerated expansion creating energy

[friend]

If the universe is accelerating in its expansion, and galaxies are increasing their speed away from each other, does that mean that the kinetic energy of the galaxies are increasing with the increase in the expansion rate? If so it would seem that the energy of the universe is increasing. Is this right? Thanks.

 

[mfb]

Well, kinetic energy in which frame? In their local frame of rest with respect to the cosmic microwave background, they are not accelerating. We observe a red-shift, which we can relate to some velocity value. But this has no direct physical meaning, at least for galaxies far away. Relative to coordinates which expand together with space, those galaxies are (nearly) at rest.

 

[Naty1]

Short answer: probably not. Nobody really knows. Does a ball accelerating down a hill gain energy? [yes, kinetic, no total.] But the 'total energy' of the universe lies outside conservation of energy rules and regulations.

For one thing dark energy constitutes almost 3/4 of the mass-energy in the universe and we know darn little about it. For example, I don't think there is a consensus about the relationship between dark energy, the cosmological constant, vacuum energy and scalar fields.

As the universe expands, it also 'cools'...otherwise we'd still be at the approximate 3,000 degres Kelvin that the cosmic microwave was emitted at about 13.7B years ago. [The CMBR is now a lot longer wavelength than it used to be and continues to get longer.] And the universe has expanded and acclerated a lot faster in the past than it is now. So it seems things are cooling, but of course that is only one component of 'total energy'.

Another 'clue' is that most scientists believe we'll end up in a cold dark empty universe many billions of years from now. But that will be a state of maximum entropy not necessarily a different total energy. A further clue is that none of the 'cosmological calculators' available online provide a way to calculate the 'total energy' of the universe. One more technical answer, indicating 'we do not have a good answer', comes from PeterDonis of these forums:

QUOTE]... energy "conservation" is more complicated:

* In a stationary spacetime (i.e., one with a time translation symmetry), one can define a conserved "total energy" using the time translation symmetry and Noether's theorem.

* In an asymptotically flat spacetime (i.e., one in which the metric approaches the Minkowski metric at large "distances" from some central region), one can define a conserved "total energy" by finding an effective 4-momentum vector for the system in the asymptotically flat metric. Since this basically amounts to finding an asymptotic time translation symmetry, it ends up being basically equivalent to the stationary case above.

* In a spacetime that is neither stationary nor asymptotically flat, such as in the FRW spacetimes used to describe our expanding universe, neither of the above applies, so there is no good way to define a conserved "total energy".[/QUOTE]

My notes don't indicate the source for this..maybe also Peter:

In *all* of the above cases, there are various ways to define "energy stored in the gravitational field", and with at least some of them, you can often come up with a "conservation law" that includes energy being "exchanged between matter and the gravitational field". However, none of these "conservation laws" are relativistically covariant; they all require picking a particular coordinate chart and treating it as "special" somehow. [This last sentence refers to the 'frame' of reference in post #2.]

 

[Chronos]

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 due to expansion is an illusion. All galaxies have a fixed amount of kinetic energy within there own local reference frame.

 

[clamtrox]

One thing to note is that the energy in expansion of space is not kinetic, it's potential; just like with an apple hanging from a tree on Earth. As you may remember, potential energy is actually negative! But then you must also remember that dark energy has a positive energy density (hence the name!). It turns out, in a flat universe, these two always cancel each other.

So in short, the energy stored in the expansion of the universe increases, but it's balanced by the increase in dark energy itself.

 

[friend]

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 due to expansion is an illusion. All galaxies have a fixed amount of kinetic energy within there own local reference frame.

If dark energy were to all of a sudden turn off, would the momentum of the galaxies cause them to continue to recede at their present rate. Suppose the cosmological constant term in GR were time dependent in such a way that at some time it instantly dropped to zero an stayed there. The recession speed of the galaxies would not increase when the dark energy turned off, but would they continue to recede at their present rate? Would that be due to their momentum of kinetic energy?

 

[clamtrox]

If dark energy were to all of a sudden turn off, would the momentum of the galaxies cause them to continue to recede at their present rate. Suppose the cosmological constant term in GR were time dependent in such a way that at some time it instantly dropped to zero an stayed there. The recession speed of the galaxies would not increase when the dark energy turned off, but would they continue to recede at their present rate? Would that be due to their momentum of kinetic energy?

By "turn off", do you mean vanish completely, or decay into other stuff? The Friedmann equation that governs the expansion rate is H^2 = \rho where H is the expansion rate and \rho is the energy density of the ideal fluid the universe is filled with (written in convenient units). If you change the energy density on the right hand side (dark energy vanishes completely), then you change expansion rate on the left hand side. On the other hand, if the dark energy just decays into something else (RHS does not change), then expansion rate does not change either. What would change in both cases is the time evolution of H.

 

[Mark M]

If dark energy were to all of a sudden turn off, would the momentum of the galaxies cause them to continue to recede at their present rate. Suppose the cosmological constant term in GR were time dependent in such a way that at some time it instantly dropped to zero an stayed there. The recession speed of the galaxies would not increase when the dark energy turned off, but would they continue to recede at their present rate? Would that be due to their momentum of kinetic energy?

Dark energy is NOT the reason the universe is expanding. It's the reason the universe is accelerating. General relativity requires spaces filled with homogenous distributions of matter to expand, in the FRW metric.

Adding a negative pressure cosmological fluid (or cosmo constant) will accelerate this expansion.

 

[bcrowell]

FAQ: https://www.physicsforums.com/showthread.php?t=506985

 

[Naty1]

friend:

If dark energy were to all of a sudden turn off, would the momentum of the galaxies cause them to continue to recede at their present rate. ...Would that be due to their momentum of kinetic energy?

no. no. [There is no such thing in physics as 'momentum of kinetic energy' but I think I know what you are asking.]

I suspect your real question is more like "If the causes of expansion and acceleration of the universe were to shut off..." etc.
edit: Upon further consideration, I now think this is a hypothetical impossibility. See below.

In that case it does NOT appear the galaxies would move apart. In general, galaxies are pretty much at rest with respect to expansion, that is locally; they have no special local motion except their local motion. So if the intervening space 'stopped expanding', so would measurements of their relative separations.

 

[George Jones]

In that case it does NOT appear the galaxies would move apart. In general, galaxies are pretty much at rest with respect to expansion, that is locally; they have no special local motion except their local motion. So if the intervening space 'stopped expanding', so would measurements of their relative separations.

This is incorrect. There exist expending universes that don't have dark energy (see the post by Mark M)!

In this case (neglecting radiation):

1) solve the Friedmann equation for a universe that has matter and dark energy;

2) solve the Friedmann equation for a universe that only has matter;

3) match the solutions smoothly at the time the matter "disappears" (assuming the "vanish completely: scenario of clamtrox's post).

The universe continues to expand after dark energy completely disappears. If there is enough matter the expansion will eventually stop, but this will happen sometime after the drak energy disappears.

 

[Naty1]

George, Thank you: I probably don't understand the subtely of your reply, but maybe my comment below covers it.

In rereading my own statements, I now realize I created a hypothetical impossibility...

"If the causes of expansion and acceleration of the universe were to shut off..." etc.

In that case it does NOT appear the galaxies would move apart. In general, galaxies are pretty much at rest with respect to expansion, that is locally; they have no special local motion except their local motion. So if the intervening space 'stopped expanding', so would measurements of their relative separations.

No matter what we 'shut off', the [approximate] homogeneity and isotropic character of the large scale universe remains and so expansion continues...I was incorrectly thinking about shutting down the cosmological constant...

So I did and do agree with MarkM's post:

General relativity requires spaces filled with homogenous distributions of matter to expand, in the FRW metric.

so expansion continues...

 

[friend]

Well, some think that the dark energy will increase exponentially until atoms rip apart. Maybe at that time it would be more clear that the kinetic energy of stuff will increase as everything starts accelerating away from each other on a more local scale.

 

[Drakkith]

Well, some think that the dark energy will increase exponentially until atoms rip apart. Maybe at that time it would be more clear that the kinetic energy of stuff will increase as everything starts accelerating away from each other on a more local scale.

I don't think the expansion creates kinetic energy. Objects are receding from each other, but they never approach anything else.

 

[Mark M]

I don't think the expansion creates kinetic energy. Objects are receding from each other, but they never approach anything else.

Right. The metric of space is expanding, so that the distance in between galaxies is increasing. The galaxies themselves aren't moving (though they do have some 'peculiar' motion unrelated to the expansion). So, they don't have any extra kinetic energy.