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

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

Notes on interacting holographic dark energy model in a closed universe

We consider interacting holographic dark energy model in Friedmann Robertson Walker space time with positive spatial curvature and investigate the behavior of curvature parameter and dark energy density in accelerated expanding epoch. We also derive some conditions needed to cross the phantom divide line in this model.Comment: 10 pages, typos corrected, some explanations and references added and updated, accepted for publication in JCA