Up close, the universe is very inhomogeneous. There is the odd very-dense star or planet, but most of it is mostly empty space - vacuum. But, as we zoom out, we expect different large chunks of space to be similar. These chunks must be very large, because we know that matter clusters in solar systems, galaxies, and even galactic clusters.
If the universe is indeed homogenous, with matter evenly distributed, then one might think that there is no reason to think our local neighborhood is special. But, there are a couple of reasons to think that this isn't true. The first is the anthropic principle. We live in a place that supports human life - on a planet orbiting a star. That puts us in a galaxy which is in a galactic supercluster. There may be isolated stars not in galaxies (ejected from galaxies, or ?), but they are rare, and the odds favor stars in galaxies. The fact that we are in a galactic supercluster means we are surrounded by more matter than a random point in the universe, at least unless we average over a very large volume.
This discussion is important for astrophysicists - especially cosmic-ray enthusiasts because not everything we study comes from far away. Charged-particle cosmic rays (protons or heavier particles) come mostly from our galaxy, with the most energetic ones likely coming from other nearby galaxies. Gamma-rays also mostly come from our galaxy. In contrast, neutrinos can come from far more distant sources. So, if we want to compare the neutrino rate with the extremely high-energy (i. e. extragalactic) cosmic-ray rate, we have to account for the fact that the cosmic-rays come from a higher-density region of space (i. e. our relatively local neighborhood) than the neutrinos, which come from a much larger volume.
That said, it is not easy to quantify the increase in density, since our measurement methods necessarily vary with distance. A 2009 paper, Andrea Silvestri and Steve Barwick (both at UC Irvine) looked at this effect. The published version, in Phys. Rev. D is available here, while the freely available arXiv version is available here. Silvestri and Barwick argued that, for rare neutrino sources (if they are rare, then they are well separated, and likely far from us), more than 5 Mpc (megaparsecs) away, there is no anthropic increase in density, but, at smaller distances, the density increase is significant, about 5.3. Other groups have had different somewhat different estimates; As our neutrino measurements become more precise, it will be necessary to investigate this bias in more detail.
In my next post, I will discuss a closely related question: does the universe look the same in all directions?