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

The energy densities of matter and the vacuum are currently observed to be of the same order of magnitude: $(\Omega_{m 0} \approx 0.3) \sim (\Omega_{\Lambda 0} \approx 0.7)$. 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.Comment: Submitted to Ap

Dark-Energy Dynamics Required to Solve the Cosmic Coincidence

Dynamic dark energy (DDE) models are often designed to solve the cosmic coincidence (why, just now, is the dark energy density $\rho_{de}$, the same order of magnitude as the matter density $\rho_m$?) by guaranteeing $\rho_{de} \sim \rho_m$ for significant fractions of the age of the universe. This typically entails ad-hoc tracking or oscillatory behaviour in the model. However, such behaviour is neither sufficient nor necessary to solve the coincidence problem. What must be shown is that a significant fraction of observers see $\rho_{de} \sim \rho_m$. Precisely when, and for how long, must a DDE model have $\rho_{de} \sim \rho_{m}$ in order to solve the coincidence? We explore the coincidence problem in dynamic dark energy models using the temporal distribution of terrestrial-planet-bound observers. We find that any dark energy model fitting current observational constraints on $\rho_{de}$ and the equation of state parameters $w_0$ and $w_a$, does have $\rho_{de} \sim \rho_m$ for a large fraction of observers in the universe. This demotivates DDE models specifically designed to solve the coincidence using long or repeated periods of $\rho_{de} \sim \rho_m$.Comment: 16 pages, 8 figures, Submitted to Phys. Rev.

A comprehensive comparison of the Sun to other stars: searching for self-selection effects

If the origin of life and the evolution of observers on a planet is favoured by atypical properties of a planet's host star, we would expect our Sun to be atypical with respect to such properties. The Sun has been described by previous studies as both typical and atypical. In an effort to reduce this ambiguity and quantify how typical the Sun is, we identify eleven maximally-independent properties that have plausible correlations with habitability, and that have been observed by, or can be derived from, sufficiently large, currently available and representative stellar surveys. By comparing solar values for the eleven properties, to the resultant stellar distributions, we make the most comprehensive comparison of the Sun to other stars. The two most atypical properties of the Sun are its mass and orbit. The Sun is more massive than 95 -/+ 2% of nearby stars and its orbit around the Galaxy is less eccentric than 93 +/- 1% of FGK stars within 40 parsecs. Despite these apparently atypical properties, a chi^2 -analysis of the Sun's values for eleven properties, taken together, yields a solar chi^2 = 8.39 +/- 0.96. If a star is chosen at random, the probability that it will have a lower value (be more typical) than the Sun, with respect to the eleven properties analysed here, is only 29 +/- 11%. These values quantify, and are consistent with, the idea that the Sun is a typical star. If we have sampled all reasonable properties associated with habitability, our result suggests that there are no special requirements for a star to host a planet with life.Comment: Published in the Astrophysical Journal, 684:691-706, 2008 September 1. This version corrects two small errors the press could not correct before publication - the errors are addressed in an erratum ApJ will release on Dec 1, 200