The discussion centers on the relationship between the expansion of the universe, dark energy, and the conservation of energy. It establishes that, according to General Relativity (GR), there is no global conservation of energy due to the time-dependent Friedmann-Robertson-Walker (FRW) metric, which allows for local conservation represented by the equation \nabla_{\mu}T^{\mu\nu}=0. From a Newtonian perspective, the increase in dark energy as the universe expands is counterbalanced by negative pressure work, resulting in energy conservation. The conversation highlights the complexities of energy conservation in cosmological contexts.
PREREQUISITESAstronomers, physicists, cosmologists, and students interested in the implications of dark energy and the fundamentals of General Relativity.
nicksauce said:GR point of view: There is no global conservation in the universe, because the FRW metric is time dependent. In GR there is only local energy conservation enforced by \nabla_{\mu}T^{\mu\nu}=0, and adding a term to the stress tensor of the form \Lambda\,g_{\mu\nu} doesn't change that.
Newtonian point of view: As the universe gets bigger, there is more energy from dark energy. However, as the universe gets bigger, PdV work is done on it by sources of pressure. Since dark energy has a negative pressure, this work is negative, and so the two energies exactly cancel out to conserve energy.