# Confusing descriptions of an "expanding" universe

• I

## Main Question or Discussion Point

It seems like the following sentence implies that 'dark energy' *(assuming that is the cause of the acceleration) is infinite:

"the universe appears to be expanding at an increasing rate, so that the velocity at which a distant galaxy is receding from the observer is continuously increasing with time."

Wouldn't this phenomenon require an infinite source of energy? A force which can continuously accelerate an object (let alone the entire universe) would need to be infinite itself... But wouldn't that violate some thermodynamic law (probably the second) or some conservation principle? How can we have infinite energy in a closed finite universe?!

Or am I misunderstanding the word "expanding," and/or misusing the word "acceleration" here?

Thanks

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How can we have infinite energy in a closed finite universe?!
Who told you the universe was closed and finite? That is not the case, actually it is thought of as flat and infinite.

Who told you the universe was closed and finite? That is not the case, actually it is thought of as flat and infinite.
Let's deal with that next (because we don't know if the universe is infinite either), but first I want to know: Does that sentence imply dark energy is infinite?

It has a power of ρcrit·ΩΛ·c²=5·10⁻¹⁰ Joule per cubic meter (because of the growth of m³ a volume with the radius of the moon's orbit around the earth generates a power of roughly 1 Watt). ρcrit is the critical density, ΩΛ the fraction of dark energy and c of course the speed of light. If the universe is infinite, you have an infininte amount of cubic meters, so the total energy alone would already be infinite (but so would be the total number and mass of all stars in an infinite universe). If the universe is spatially finite, but temporally infinite, the total energy produced would be 1 Watt times a finite number of volumes times infinitely many seconds = infinity. But since the total energy in an expanding universe is not conserved (photons for example lose energy proportionally to the growth of the scalefactor) that is not a problem since after every given time the total energy produced would still be finite (you never reach temporal infinity).

• Ghost117
PeterDonis
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Wouldn't this phenomenon require an infinite source of energy?
No.

A force
There is no force involved. All of the galaxies in the universe are moving on geodesics--they are in free fall. The effect of dark energy is on the geometry of spacetime as a whole--it produces a geometry in which the geodesics are diverging, and the rate of divergence of nearby geodesics increases with time along any one of them.

am I misunderstanding the word "expanding," and/or misusing the word "acceleration" here?
Yes. See above.

• Ghost117
It has a power of ρcrit·ΩΛ·c²=5·10⁻¹⁰ Joule per cubic meter (because of the growth of m³ a volume with the radius of the moon's orbit around the earth generates a power of roughly 1 Watt). ρcrit is the critical density, ΩΛ the fraction of dark energy and c of course the speed of light. If the universe is infinite, you have an infininte amount of cubic meters, so the total energy alone would already be infinite (but so would be the total number and mass of all stars in an infinite universe). If the universe is spatially finite, but temporally infinite, the total energy produced would be 1 Watt times a finite number of volumes times infinitely many seconds = infinity. But since the total energy in an expanding universe is not conserved (photons for example lose energy proportionally to the growth of the scalefactor) that is not a problem since after every given time the total energy produced would still be finite (you never reach temporal infinity).
Okay, I think I understand: Since m³ is in the denominator, it keeps the result from going to infinity.

In English:
1. In a finite expanding universe, the limit would not go to infinity, because the scale of space increases along with the added energy...
2. The extra energy isn't magically appearing from somewhere outside the universe, because it is generated intrinsically by the empty space itself..
3. The energy delta is actually negative, because of #1 (e.g. the case of photons you mentioned).
Please correct me if I misunderstood you on any of these points.

Now with that said, yes, in an infinite universe, all this would be moot anyway, since infinite energy isn't an issue there.

There is no force involved. All of the galaxies in the universe are moving on geodesics--they are in free fall. The effect of dark energy is on the geometry of spacetime as a whole--it produces a geometry in which the geodesics are diverging, and the rate of divergence of nearby geodesics increases with time along any one of them.
Yes the geometery of spacetime in GR has replaced the "force" model in cosmology. But I just wanted to know if the oldschool Newtonian "force" model yielded the implication I was getting at all.... Apparently it doesn't, given my understanding of Yukterez's 'proof' above (assuming I understood it lol.)

PeterDonis
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It has a power of
Where does this come from? Do you have a reference?

It has a power of ρcrit·ΩΛ·c²=5·10⁻¹⁰ Joule per cubic meter (because of the growth of m³ a volume with the radius of the moon's orbit around the earth generates a power of roughly 1 Watt). ρcrit is the critical density, ΩΛ the fraction of dark energy and c of course the speed of light. If the universe is infinite, you have an infininte amount of cubic meters, so the total energy alone would already be infinite (but so would be the total number and mass of all stars in an infinite universe). If the universe is spatially finite, but temporally infinite, the total energy produced would be 1 Watt times a finite number of volumes times infinitely many seconds = infinity. But since the total energy in an expanding universe is not conserved (photons for example lose energy proportionally to the growth of the scalefactor) that is not a problem since after every given time the total energy produced would still be finite (you never reach temporal infinity).
Where does this come from? Do you have a reference?
There are no references, normally only crackpots talk about the power of dark energy

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PeterDonis
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There are no references, normally only crackpots talk about the power of dark energy
Which means you should not be posting about it here.