Energy conservation in an expanding Universe

[kasperm]

How is energy conserved in an expanding universe? As space expands between, say, stars in a galaxy, don't they gain potential energy in the gravitational field of the galaxy? Which mechanism lessens the total kinetic energy?

 

[Matterwave]

Usually, that would be gravity. As the Universe expands, one would expect gravity to slow down the expansion. However, with the discovery of so called "dark energy", we found that the expansion is not slowing, but speeding up.

The energy conservation ramifications of this discovery is a mystery to me...perhaps someone more knowledgeable can answer you better.

 

[edpell]

I still like conservation of energy. There are many on PF that say conservation of energy is only true locally. I would like to see a reference for that.

It does seem that "dark energy" does increase the total energy of the universe. It seems a lot like spontaneous creation of matter or the spontaneous creation of maggots in rotting meat. Basically magic.

 

[Chalnoth]

How is energy conserved in an expanding universe? As space expands between, say, stars in a galaxy, don't they gain potential energy in the gravitational field of the galaxy? Which mechanism lessens the total kinetic energy?

Well, energy conservation isn't terribly simple in curved space-time. If you want a good, fairly in-depth description of what's going on here, take a look at this:
http://www.obscure.org/physics-faq/Relativity/GR/energy_gr.html

 

[Chronos]

I'm with you edpell. IMO, the energy content of the universe is essentially fixed [save for dark energy]. Expansion merely dilutes it.

 

[Chalnoth]

I'm with you edpell. IMO, the energy content of the universe is essentially fixed [save for dark energy]. Expansion merely dilutes it.

Not quite. Normal matter does this because it is largely pressureless. But any matter that experiences pressure (such as photons) loses energy per comoving volume.

 

[kasperm]

Im sorry, my question might have been a bit unclear.

Consider this: Two stars a unit distance apart has a well defined potential energy in their gravitational field, or equivalently, a well defined amount of work needs to be done against the field to move each of them from the center of mass out to their respective positions. If we wait a given amount of time and measure their distance once again, it will have increased due to the expansion of the universe so the amount of work need to move them from CoM to their new positions has increased proportionally. So my question is, which mechanism ensures energy conservation given the increased potential energy?

(or perhaps my question fundamentally flawed?)

 

[Chalnoth]

Im sorry, my question might have been a bit unclear.

Consider this: Two stars a unit distance apart has a well defined potential energy in their gravitational field, or equivalently, a well defined amount of work needs to be done against the field to move each of them from the center of mass out to their respective positions. If we wait a given amount of time and measure their distance once again, it will have increased due to the expansion of the universe so the amount of work need to move them from CoM to their new positions has increased proportionally.

Well, there are a couple of different issues here. First, if the two are in orbit around one another, they won't be affected at all by the expansion. If the two are far away, and there is no dark energy, then they will simply coast along away from one another, slowing down the entire way. It's only with the existence of dark energy that things start to get a little weird.

But in that case, the fundamental flaw with your analysis is that the potential energy is not well-defined in General Relativity. See the article I posted earlier.

 

[yogi]

Ed Tryon was probably the first to advance the idea that the total energy of the universe is always zero - specifically the potential gravitational energy at all times is balanced by the expansion energy. Within the Hubble sphere, equating the 1/2 mv^2 energy of each shell of the expansion using Hubble's law to the potential results in a required matter content equal the critical density of an Einstein - de Sitter universe

 

[Chalnoth]

Ed Tryon was probably the first to advance the idea that the total energy of the universe is always zero - specifically the potential gravitational energy at all times is balanced by the expansion energy. Within the Hubble sphere, equating the 1/2 mv^2 energy of each shell of the expansion using Hubble's law to the potential results in a required matter content equal the critical density of an Einstein - de Sitter universe

Well, bear in mind that this statement is only true for a closed universe.

 

[kasperm]

the fundamental flaw with your analysis is that the potential energy is not well-defined in General Relativity.

This makes sense. So this is why people say energy is conserved on a local scale but not on large scales?

@yogi: Interesting, I wasnt aware of that idea. Will check it out.

 

[Chalnoth]

This makes sense. So this is why people say energy is conserved on a local scale but not on large scales?

Well, locally, any space-time is flat. In flat space-time, energy is conserved.