Robert Foster asked:
Do maps showing galaxy distributions of the universe correct for where they are now. ie an image of a Galaxy 3.5 billion yrs has had 3.5 billion yrs to move to its actual position at this instant in time. How would this affect the maps produced. ?
Our 3D maps of galaxy distribution are actually maps of direction and redshift. We assume that distance is proportional to redshift and that the redshift is entirely due to Doppler effect. Those assumptions allow us to translate redshift to distance. The maps also assume that the objects are stationary relative to the comoving space around them, since we have no way to detect whether they are or not. We can detect radial motion of nearby galaxies, so we know they do move; but that relative motion is tiny compared to the expansion of space between us and the more distant galaxies.