Coincidence Problems And Dark Energy.

(The third post in the dark energy series.)

One issue that comes up in discussions about the cosmological constant is the coincidence problem.  If dark energy is really caused by a cosmological constant, we seem to be living in a very special place in the universe's history.  Here is an explanation by the the Wikipedia:

The cosmic coincidence problem asks why the cosmic acceleration began when it did. If cosmic acceleration began earlier in the universe, structures such as galaxies would never have had time to form and life, at least as we know it, would never have had a chance to exist. Proponents of the anthropic principle view this as support for their arguments. However, many models of quintessence have a so-called tracker behavior, which solves this problem. In these models, the quintessence field has a density which closely tracks (but is less than) the radiation density until matter-radiation equality, which triggers quintessence to start behaving as dark energy, eventually dominating the universe. This naturally sets the low energy scale of the dark energy.

The point is, many people don't like the idea that dark energy is related to the cosmological constant because if was, it seems like we live in a special place in the universe.  But physicts have been trained to not like theories where we appear to be in a special place.  This causes many to adopt models like quntessesnce where this problem goes away. (Quintessence being the idea that dark energy is related to an oscillating filed, not a constant.)

However, remember, these posts are in favor of the cosmological constant. :)  This is a response. (Beyond the fact that no data supports/suggests quintessence is real. Seriously people!)

Back to the paper:

Say we want to hold a “cosmological principle” stating that we are not in a special place in the universe, in space or in time. Thus, there is a contradiction between the ΛCDM model and such a cosmological principle: to believe that the observed acceleration is caused by a cosmological term in Einstein equations requires us to believe also that we are in a very special moment of the history of the universe. This is the “coincidence argument” against the cosmological constant scenario.

The authors critique this "problem" in a couple of ways.  I am only going to highlight the second:

The cosmological principle cannot be applied uncritically... For instance, a rigorous application of the cosmological principle would lead us to expect that the density around us must be of the same order of magnitude as the average density of the universe (which is manifestly false); or, to put it visually, that the Earth is mostly covered by land and not oceans (most humans observe land and not water around them.)

Humans do not live in a random location on Earth. They leave on land and not on water. Our civilization is not located in a random location in the universe: it is located on a very high peak on the density fluctuations, far out of statistics. This observation is a very mild form of anthropic principle. This is a form of anthropic principle that cannot be rejected even by those (like us) who most furiously oppose the use of anthropic-principle arguments in theoretical physics.

The point is:

1. Physicists like assuming we don't live in a special place in the universe, in space and in time.
2. But the fact that we are in a galaxy means we are in a very special place.  (Most points in the universe are not inside galaxies.)
3. The fact that we are on an earth at just the right distance to a star for life means we are in a very special place.
4. The fact that we live on land when 2/3 of the earth is water means we live in a very special place.
5. Etc...

So there are real limits in applying cosmological principle.  We don't always get the right answer if we assume it.  Sometimes we do have to accept this "weak" form of the anthropic principle that in order to exist we do need to be in a special place.

In a universe with the of value of λ like in our universe, it is quite reasonable that humans exist during those 10 or so billions years when Ωb and Ωλ are within a few orders of magnitude from each other. Not much earlier, when there is nothing like the Earth, not much later when stars like ours will be dying. Of course there is nothing rigorous in these arguments. But this is precisely the point: there is nothing rigorous or convincing in the coincidence argument.

So, to be alive we need to be in a special place.  We need to be in a galaxy.  We need to be the right distance from a star.  And so maybe we should not be shocked to discover we are also living in a special time when the Ωb and Ωλ are within a few orders of magnitude from each other.  These values are needed for life as much as existing inside galaxies or on warm planets is.

However, I admit we are not sure, and anthropic arguments are often not satisfying. (But again, philosophical arguments aside: not data suggesting anything like quintessence is real.)