In my cosmology model, the observable universe has almost all its mass in a spherical shell of plasma situated near the Hubble radius (also the Schwarzschild radius for the universe black hole). The remaining mass is in the interior galaxies and gas/dust clouds. I have questions concerning the nature of the metric in the interior and whether or not an observer at our position would see gravitational time dilation in events nearer to the shell.
We can use Newtonian gravity in the cosmic case as the distances are so large. From the shell theorem, the gravitational forces inside the shell would cancel out. Turning it back towards general relativity, however, would this mean that gravitational time dilation would not be seen in sources nearer the shell? Or would it be more accurate to invoke time dilation due to the deeper gravitational potential well nearer the shell. If we wanted to describe the interior metric, would we best call it flat and Minkowski, Schwarzschild, de Sitter or what?
Sorry if this all sounds a bit vague!
I asked a question in Q & A (discussion 199) about this and it was determined that there would be no gravitational redshift or time dilation related to the shell.