Is the Hubble Ultra-Deep Field image representative of the entire sky?

Question

The Hubble ultra-deep field image is a photograph of an area of sky equivalent to a 1mm x 1mm piece of paper held a metre away from the eye (one thirteen millionth of the entire sky). It contains an estimated 10,000 galaxies.

If galaxies were uniformly distributed, and the HUDF were representative of the entire sky, that would mean there were approximately 130 billion galaxies, which falls between estimates I have read of between 100 and 200 billion as the total number of galaxies.

However, my understanding is that galaxies occur in clusters, which would seem to imply that some areas of the sky should be more densely populated than others.

So is the HUDF representative of the entire sky, or are some areas much more and much less densely populated?

Answer 1

Short answer: both.

HUDF is representative on the type of galaxies we can find at that distance (and remember that distance also means time ago).

On the other hand, we do not really know how the galaxies are grouped beyond certain level, but we think they are grouped on so-called filaments, leaving enormous empty voids.

In this sense, HUDF's density does not represent the entire sky.

http://cosmicweb.uchicago.edu/filaments.html

Answer 2

HUDF suffers from cosmic variance. So while you could choose what you believe is a random and unbiased region of sky, your uncertainty will be larger than just the standard statistical sampling error. There would be additional uncertainty because of large scale structure since galaxies are not randomly distributed on the sky.