Expansion of the Universe, Dark Energy and Conservation of energy.

[xdrgnh]

Doesn't the expansion of the universe defy conservation of energy, as the universe expands more dark energy is being created. That means the total energy in the universe isn't stable and is increasing.

 

[nicksauce]

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.

 

[xdrgnh]

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.

Thanks for clarifying that up for me, I really appreciate it. I'm interesting that tensor equation you showed me. I'm not really familiar with tensors, I do know partial derivatives though can you explain that equation more throughly for me.