With accelerated expansion of universe which is same in all direction we know that dark energy increase with time because space between any two point in space time increases with time. So after some finite time we can not see nearby galaxy cluster which we can see now. So doesn't that violate conservation of energy which says energy neither can created nor can destroyed. Because with expanding universe energy in the form of dark energy increases with time so if we consider whole universe (visible + invisible) as isolated system then energy of whole universe increase means energy is created from nothing. Am I missing something over here?
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2possible duplicate of How is dark energy consistent with conservation of mass and energy? – Apr 05 '14 at 17:10
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Friedmann-type universes have zero total energy - the positive contributions by matter and dark energy are cancelled by the negative contribution due to gravitational energy – Christoph Apr 05 '14 at 17:48
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possible duplicate of Conservation law of energy and Big Bang? – John Rennie Apr 05 '14 at 17:52
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See the link I've suggested. The FLRW metric that (we think) describes our universe is time dependant and this means energy is not conserved. – John Rennie Apr 05 '14 at 17:53
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This article by John Baez might be of interest as background reading. – John Rennie Apr 05 '14 at 18:18
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@JohnRennie: I disagree with energy not being conserved in FLRW cosmology; the relevant papers are linked from this comment – Christoph Apr 05 '14 at 18:25
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@Christoph the lack of time translation symmetry removes the energy conservation law from FLRW or other universes whose geometry is time-dependent – Jim Apr 05 '14 at 18:33
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@Christoph: I note the question you've linked contains contrary opinions from Phil Gibbs and Luboš Motl. They are both vastly better physicists than I will ever be, so how am I to judge who is right? The impression I get is that whether energy is conserved or not depends on exactly what you count as energy. You would have to concede there is no time shift symmetry, so we cannot simply shout Noether's theorem and wave our arms. – John Rennie Apr 05 '14 at 18:38
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@JohnRennie: you can read more of Philip and Luboš in the comments of Philip's blog posts on energy conservation in GR ( http://blog.vixra.org/2010/08/06/energy-is-conserved/ http://blog.vixra.org/2010/08/08/energy-is-conserved-the-maths/ http://blog.vixra.org/2010/08/17/energy-is-conserved-in-cosmology/ ) – Christoph Apr 05 '14 at 19:36
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@Jim: we do not need global time translation symmetry in GR - the time-like vector field of your choice basically becomes a gauge parameter – Christoph Apr 05 '14 at 19:50
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First, in the most common model of dark energy, $\Lambda$CDM, dark energy is a constant energy density, which means that the "energy" from dark energy does increase as the universe expands. Second, the law of conservation of Energy is only valid in a static universe. Because our universe is expanding, it is no longer the same at every moment of time and so energy need not be conserved. The conserved quantity is, instead, the stress-energy.
In this way, you are quite right, energy is not conserved, but it doesn't have to be. On small scales, the conservation of energy law still applies, but on scales where dark energy becomes important, there is no such law.
Jim
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It is not true that "the law of conservation of Energy is only valid in a static universe" – Philip Gibbs - inactive Apr 19 '14 at 11:38