Conservation of Energy on the Cosmological Scale

[Islam Hassan]

Am I correct in understanding that locally, ie, with respect to circumscribable phenomena, conservation of energy is valid in the cosmos but that otherwise it is/may not be?

Otherwise said, the source of dark energy does/may not obey this principle? Or is this a question that does not fall within the definable scope of present-day cosmology?IH

 

[PeterDonis]

Conservation of energy in General Relativity means that the covariant divergence of the stress-energy tensor is zero. Physically, this means that stress-energy cannot be created or destroyed in any infinitesimal volume of spacetime. This is true for all types of stress-energy, including dark energy. This conservation law is local.

In a general curved spacetime, there is no global energy conservation law for stress-energy. Sean Carroll gives a good discussion of this here:

http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/

 

[haushofer]

Am I correct in understanding that locally, ie, with respect to circumscribable phenomena, conservation of energy is valid in the cosmos but that otherwise it is/may not be?

Otherwise said, the source of dark energy does/may not obey this principle? Or is this a question that does not fall within the definable scope of present-day cosmology?IH

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.