Last week, we enjoyed a seminar by Dr. Navin Sivanandam, a postdoc at AIMS, about his latest paper. Navin’s surprising answer to the above question is no, the cosmological coincidence is not something we should concern ourselves with.
He uses a version of the anthropic principle citing Carter (1974) who argued “the Universe is consistent with life” and Vilenkin (1995) who said “we should be typical amongst observers”. These are statements about the prior we should apply, an important point since we only have one Universe so the prior dominates.
In order to calculate just how likely it is to have cosmologists such as us observing a cosmological coincidence as we do, the anthropic principle has to be altered. We should not sample uniformly from all universes, but sample uniformly from the space of all observers. This makes a type of universe with many observers more likely to be sampled.
There already exist some possible solutions such as that of Garriga, where observers are more likely to occur around the epoch of carbon production, and that of Lineweaver and Egan, where similarly observers are more likely to exist around the epoch when many planets exist. These arguments have some problems, such as assuming that life must be similar to us and it may force observers to live in the late future.
Navin has proposed a novel approach: “a measurement of a quantity should be typical of all measurements of that quantity”, which bypasses the issues of discussing specific observers. When Navin computes the probability of measuring the ratio of matter density to dark energy density that we measure (assuming a cosmolgical constant), he finds that the most likely time for cosmologists to exist is now, when we measure a cosmological coincidence. This comes from the fact that we are more likely to make cosmological observations when it is easy to measure expansion. Thus the universe must be at an age when objects are far enough away to detect the expansion, but not so far that too many objects are outside the observable universe.
Thus, using the probabilities calculated, Navin makes the bold claim that the coincidence problem is not a problem at all.