# What is meant by “Energy is exactly conserved locally in GR. Inflation and Dark Energy isn't an exception to this.”?

In Ben Crowell’s comments in these threads

Attractive gravity has negative energy, what about repulsive gravity in the inflation phase?

Does the fact that energy is not conserved in cosmology open the possibility of new matter/atoms being created in the universe?

What is meant by ”Energy is conserved locally in GR. Inflation and Dark Energy isn't an exception to this.”?

Does it mean that inflation and dark energy can’t create new energy to maintain its constant energy density because of local conservation?

I fear that I have badly misunderstood the comments.

• You should probably ask the authors directly. Note that GR locally is SR, and in SR energy is conserved. Note that "locally" includes time, so delta-t should be small enough that space doesn't expand enough to have a measurable effect. – johndecker Jul 18 '18 at 9:19
• The author probably means that the covariant derivative of the stress-energy tensor vanishes. So does the covariant derivative of Einstein’s cosmological constant term (“dark energy”). – Bert Barrois Jul 20 '18 at 11:01

In a matter dominated Universe on scales much smaller than the Hubble length ($\approx 4$ Gpc), and not near dense collapsed objects like neutron stars and black holes, the standard assumption is that one can use Newtonian physics and so energy is conserved on those small scales. One can also accommodate a cosmological constant by adding a repulsive force which increases with distance. As this can be accomplished by a potential proportional to distance squared you can still have energy conservation by exchanging kinetic and potential energy.