i have been studying cosmology from this source :

https://www.astro.ucla.edu/~wright/cosmo_02.htm
... and have a problem with this part :
(( dynamics ... ))

With a constant mass interior to D(t) producing the acceleration of the edge (...)

The problem i have is they describe the situation as symmetric from the center of a sphere and try to apply this symmetry to the edge of the sphere while, since galaxies are escaping at relativistic velocities, the situation at the edge cannot be described as symmetric in the way that would imply that :

The gravitational effect of the external matter vanishes (...)