The Cosmic Coincidence as a Temporal Selection Effect Produced by the Age Distribution of Terrestrial Planets in the Universe

Abstract

The energy densities of matter and the vacuum are currently observed to be of the same order of magnitude: $({\Omega }_{m0}\approx 0.3)\sim ({\Omega }_{\Lambda 0}\approx 0.7)$. The cosmological window of time during which this occurs is relatively narrow. Thus, we are presented with the cosmological coincidence problem: Why, just now, do these energy densities happen to be of the same order? Here we show that this apparent coincidence can be explained as a temporal selection effect produced by the age distribution of terrestrial planets in the Universe. We find a large ($\sim 68$) probability that observations made from terrestrial planets will result in finding ${\Omega }_m$ at least as close to ${\Omega }_{\Lambda }$ as we observe today. Hence, we, and any observers in the Universe who have evolved on terrestrial planets, should not be surprised to find ${\Omega }_m\sim {\Omega }_{\Lambda }$. This result is relatively robust if the time it takes an observer to evolve on a terrestrial planet is less than $\sim 10$ Gyr.

Submitted to ApJ

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