When Edwin Hubble first demonstrated the Universe was expanding in 1929, you could do a simple calculation to determine the age of the Universe. Take the rate at which galaxies expand from each other (known as the Hubble constant H) and set it equal to the inverse age of the cosmos (1/t). This simple model assumed that the Universe expands at a constant rate, thus Ht = 1. When this was first proposed within the context of the big bang model, it actually raised a few questions. Early measurements of the Hubble constant were much higher than the current accepted value, which gave a cosmic age that was actually younger than some stars.
We now know the Universe hasn’t expanded at a constant rate. The rate of cosmic expansion is determined both by dark energy driving galaxies apart, and the overall density of matter in the Universe, which tries to slow the rate of expansion. In the early universe, matter dominated, so the rate of expansion was actually decreasing. About 6.5 billion years ago the average density of the Universe dropped to the point that dark energy began to dominate, and the Universe began expanding at an ever increasing rate. An accurate determination of the age of the Universe has to account for the initial inflationary period, then deceleration, then acceleration. If you do that you get an age of about 13.8 billion years, which is the currently accepted age.
Because of this variation in cosmic expansion, the Hubble constant has changed over cosmic time. This is why you can’t simply set Ht = 1. And yet, if you take the current Hubble constant and multiply it by the currently accepted age of the Universe, you get exactly 1 (to within known uncertainties). In other words, if the Universe had expanded at a constant rate, it would be exactly the same size and age as the Universe currently is. This is known as the synchronicity problem. It’s not a problem, per se, but rather an interesting coincidence. This hasn’t been true for any other epoch of the cosmos. It’s also not the only odd coincidence. The vacuum energy density (as determined by the Hubble constant) and the matter energy density are also about equal, and is known as the coincidence problem.
As the Universe expands the matter density drops, while the vacuum density doesn’t, so it’s tempting to think that the synchronicity problem and the coincidence problem are two sides of the same coin. But a recent work shows this isn’t the case. By varying the parameters of a hypothetical universe, one could create a model where one is true but the other is not. These two unusual correlations are independent of each other. This raises the question of whether the two actually are related by some unknown physical process. We always have to be a bit careful with these kinds of questions. It is perfectly possible that the two “problems” are just due to random flukes. But when you start seeing coincidences in your data it is sometimes worth exploring.
If there is a connection, it will only be a matter of time before we find it.
Paper: Arturo Avelino and Robert P. Kirshner. The dimensionless age of the Universe: a riddle for our time. The Astrophysical Journal, Volume 828, Number 1 (2016) arXiv:1607.00002 [astro-ph.CO]