Unraveling the Mystery of Universe Expansion: Exploring External Energy Sources

[DudeWut]

So I was doing some studying and got a question on why the rate of expansion of the universe was increasing, and it got me thinking.

Newton's first law states that an object in motion will remain in motion with a constant speed unless an external force acts upon it. If the expansion of the universe is increasing, does this mean that there is an external force contributing to this acceleration? And to maintain this force, work would have to be done to maintain acceleration, so where is this extra energy coming from? If the energy was finite, stemming from the big bang, surely the acceleration would be slowing down due to the energy being used up?

What am I missing? I'm pretty sure there is something I don't know yet, still in high school haha, so could someone help me out here?

 

[mfb]

If the expansion of the universe is increasing, does this mean that there is an external force contributing to this acceleration?

No.

The expansion of the universe doesn't mean anything would move. The space between objects gets larger, this is not a motion of objects in space, and no object accelerates (on large scales). There is also no "extra energy".

 

[Gigaz]

The expansion is not conserving energy though for all we know. Galaxies gain gravitational energy when their distance increases. Particles like photons are redshifted and loose kinetic energy.

 

[DudeWut]

No.

The expansion of the universe doesn't mean anything would move. The space between objects gets larger, this is not a motion of objects in space, and no object accelerates (on large scales). There is also no "extra energy".

Alright, so what you're saying is that instead of the objects moving, the space between them stretches, like two balls on a sheet of clingfilm that is being stretched? But even so, work has to be done on whatever is in that space to be stretched and moved from rest, so won't the energy requirement for acceleration still apply?

Imagine a football. If we imagine the inflation of the football like the universe expanding, where the air inside is space and the football itself is an object. As the football is inflated further and further, eventually the pressure inside will reach a point where the football will tear. As space stretches inside a material, whether that be between atoms or what have you, would the object not eventually break under the strain of the expansion? And if it did, it would have to exert a force to overcome the different forces keeping the object together, whether that be gravity or the nuclear forces. Would this not result in work being done, and energy being used?

 

[JMz]

So I was doing some studying and got a question on why the rate of expansion of the universe was increasing, and it got me thinking.

Newton's first law states that an object in motion will remain in motion with a constant speed unless an external force acts upon it. If the expansion of the universe is increasing, does this mean that there is an external force contributing to this acceleration? And to maintain this force, work would have to be done to maintain acceleration, so where is this extra energy coming from? If the energy was finite, stemming from the big bang, surely the acceleration would be slowing down due to the energy being used up?

What am I missing? I'm pretty sure there is something I don't know yet, still in high school haha, so could someone help me out here?

Your reasoning is good, but there is some physics you don't have here. First, the expansion speed is indeed decreasing. It's probably best to think of this part as simple gravitational attraction: Even without general-relativistic effects, this would be happening, as the receding galaxies collectively pull on each other. (This would be the work that you mention.) But if they are receding fast enough compared to their mass (density), that attraction won't be enough to slow them to zero. The net energy density (kinetic energy minus gravitational potential energy, in any large volume) would be positive. In conventional orbit terms, they would have "escape velocity". Their distance would eventually increase linearly with time, though at a somewhat slower rate than now.

However, there is a very non-Newtonian effect in addition. This appears to be a constant energy density or pressure (the cosmological constant), something Einstein predicted. As far as we know, it could be positive, negative, or zero. Observably, it is tiny but positive. The result is that, instead of distances eventually increasing linearly with time, they will eventually increase exponentially with time. [That's not modern pompous usage for "much", it just means a constant growth rate: a doubling every 5 billion years, or whatever.] To be clear: Such an effect matters at cosmological distances, but it is irrelevant over smaller ones like 100 million LY. However, it does not obey a "conversation of energy" law in the ordinary sense: It does not decrease as the speed-up continues.

 

[DudeWut]

The expansion is not conserving energy though for all we know. Galaxies gain gravitational energy when their distance increases. Particles like photons are redshifted and loose kinetic energy.

Ahh, so there is a trade between the energy of fermions and the gravitational energy of the celestial body? If that is correct, would this trade off be equivalent so that no energy is created or destroyed? And if so, there is a direct interaction between the micro and the macro, could this be used to somehow investigate how the energy goes between the rules of quantum and classical physics?

 

[DudeWut]

Your reasoning is good, but there is some physics you don't have here. First, the expansion speed is indeed decreasing. It's probably best to think of this part as simple gravitational attraction: Even without general-relativistic effects, this would be happening, as the receding galaxies collectively pull on each other. (This would be the work that you mention.) But if they are receding fast enough compared to their mass (density), that attraction won't be enough to slow them to zero. The net energy density (kinetic energy minus gravitational potential energy, in any large volume) would be positive. In conventional orbit terms, they would have "escape velocity". Their distance would eventually increase linearly with time, though at a somewhat slower rate than now.

However, there is a very non-Newtonian effect in addition. This appears to be a constant energy density or pressure (the cosmological constant), something Einstein predicted. As far as we know, it could be positive, negative, or zero. Observably, it is tiny but positive. The result is that, instead of distances eventually increasing linearly with time, they will eventually increase exponentially with time. [That's not modern pompous usage for "much", it just means a constant growth rate: a doubling every 5 billion years, or whatever.] To be clear: Such an effect matters at cosmological distances, but it is irrelevant over smaller ones like 100 million LY. However, it does not obey a "conversation of energy" law in the ordinary sense: It does not decrease as the speed-up continues.

Thanks for the clear answer. So the gravitational effect of the galaxies pulling on each other increases linearly, like y=mx, slowing down expansion, but the effect of the cosmological constant is causing expansion to increase exponentially, like y=x^m? Wouldn't the effect of the cosmological constant causing an exponential increase be that eventually the growth from this would outpace the resistance that gravity would give? It seems to point to an eventual heat death, as gravity wouldn't be strong enough to counteract the effect of gravity. As the rate of expansion increases, wouldn't that also eventually become strong enough to rip apart atoms, overcoming the nuclear forces? And also, for the expansion of space like inside of an object to rip it apart to do so, wouldn't work have to be done? In which case, again, where does that energy come from? Or would the object just sort of "inflate" relative to earlier, as the space around it stretches?

 

[JMz]

Thanks for the clear answer. So the gravitational effect of the galaxies pulling on each other increases linearly, like y=mx, slowing down expansion, but the effect of the cosmological constant is causing expansion to increase exponentially, like y=x^m?

Sort of. More accurately, the gravitational force of the galaxies can be understood as ordinary 1/r^2 (we do not need curved-spacetime arguments to see the qualitative effects), just like a rocket leaving the Earth: Its speed will decrease, either to zero or, if it has sufficient initial energy, to some final escape velocity. If it "escapes", then gravity eventually becomes irrelevant, and the rocket just coasts: y(t) = mt. But exponential ~ y = a^t for some constant a and t = time (thus an ever-increasing exponent).

Wouldn't the effect of the cosmological constant causing an exponential increase be that eventually the growth from this would outpace the resistance that gravity would give? It seems to point to an eventual heat death, as gravity wouldn't be strong enough to counteract the effect of gravity.

Yes, heat death of a sort, though not quite the 19-Century thermodynamic one. This is sometimes called the Big Freeze. [Your last word gravity should have been the cosmological constant. Conventionally denoted by Λ, BTW.]

As the rate of expansion increases, wouldn't that also eventually become strong enough to rip apart atoms, overcoming the nuclear forces? And also, for the expansion of space like inside of an object to rip it apart to do so, wouldn't work have to be done? In which case, again, where does that energy come from? Or would the object just sort of "inflate" relative to earlier, as the space around it stretches?

See previous remark:

Such an effect matters at cosmological distances, but it is irrelevant over smaller ones like 100 million LY. However, it does not obey a "conversation of energy" law in the ordinary sense: It does not decrease as the speed-up continues.

In particular, it is irrelevant over distances like (a) protons, (b) molecules, (c) the Solar System, (d) the Milky Way. These systems are bound, either by (a) nuclear forces, (b) [chemical] electrical forces, (c,d) conventional gravitational forces, which are very much larger than Λ and do not decrease with time. That's unlike the slowly decreasing gravitational effect of distant galaxies as they move away, which is what allows Λ to eventually dominate the evolution.

 

[Chronos]

Let's say you were watching a football game from the endzone and notice players at the far end of the field appear to be running faster than those at the near end. Would you assume this means their energy increases with distance?