2.5 Negative Energy Density Review II

summary

Consider a thought experiment: a hollow shell allowed to collapse under its own gravity.

We attach generators to the surface of the shell using string.
As the shell collapses and the surface is pulled inward, the strings turn the generators, which produce positive power.

After its collapse, we can examine the region left between the surfaces of the old, larger shell and the new, smaller shell.

As the shell collapses and the surface is pulled inward, the strings turn the generators, which produce positive power.
To conserve energy, this gravitational field must be negative to balance out the positive power produced by the generators.

The only way conservation of energy remains intact is by showing that the energy of a gravitational field is negative.

With the generators producing outward, positive power, the only way to balance this energy is for the gravitational field to be negative.
This helps to explain why the energy density did not thin out during the exponential expansion of inflation.