The Copernican principle is a guiding foundation of cosmology. In short, it states that we are not in a privileged place in the Universe. A "random" observer will see the same Universe that we do. The cosmological standard model does satisfy this principle in space: at this moment, any other observer in the Universe should see the same Universe as we do (at large scales). Just like us, they see a smooth distribution of galaxies and a smooth CMB sky, with similar small anisotropies. However, we do live at a privileged time: in the history of the Universe, we just happen to be at the time when the dark energy density starts dominating over the dark matter density. This is known as the "coincidence" problem, and has been much discussed and agonized over. Here is a graphical description:
Today is very, very near where the two lines cross (redshift=0 is today; redshift=1,000 is where the CMB is generated; the Big Bang is at redshift=infinity). You can't even see the crossing on the main plot; you need to go to the inset to see the incredibly rapid change at redshift=1. Last week at the Yukawa Institute workshop John Moffat was advocating calling the standard model "anti-Copernican" because of this fine-tuning. He has been wanting to take matters one step further: if we are willing to break the Copernican principle in time, why not seriously consider breaking it in space instead? More on this later. The Copernican principle is one of those weird things in science that is a mix of science and aesthetics. It can't be written down as an equation. And its application is often subject to the eye of the beholder. For example, the plot above looks like a problem because we've used redshift on the x-axis to represent time. There are physically motivated reasons to use this, as it relates to the size of the Universe, and is thus a proxy for many relevant physical processes. If instead we label time the way we normally measure it (as in, on your wristwatch, if you happened to have been around since the Big Bang), you get something that looks much more reasonable:
We're no longer at a special time, and the coincidence problem vanishes. The Universe has been dark-energy dominated for billions of years, and we're nowhere near the special crossing point. So which plot is right?