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Astronomy and Cosmology
Cosmology
Conservation of Energy on the Cosmological Scale
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[QUOTE="haushofer, post: 6001227, member: 20128"] Energy conservation is subtle in GR. Without GR, we define energy as a conserved Noether current in a fixed spacetime. Spacetime is just a stage, doing nothing. However, in GR, spacetime becomes dynamical and can exchange energy with its constituents. But the subtlety is that locally, a gravitational field can always be interpreted as you accelerating. Globally this is not possible, because curvature manifests itself unambigously at a global scale. So this enables one to define energy conservation globally. For this however one needs, as in the not-GR case, symmetries. For cosmology one needs a so-called timelike Killing vector of a deSitter solution, and to my understanding such a Killing vector does not exist. The subtlety in energy conservation already follows from the observation that in an expanding spacetime with constant energy density (the cosmological constant being interpreted as an energy density!) energy seems to be created out of nothing. However, this apparent "paradox" arises from not understanding energy conservation in dynamical spacetimes. This is also Carroll's statement in Peter's link, I guess. [/QUOTE]
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Astronomy and Cosmology
Cosmology
Conservation of Energy on the Cosmological Scale
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