The degree of fine-tuning in our universe - and others

摘要

Both the fundamental constants that describe the laws of physics and the cosmological parameters that determine the properties of our universe must fall within a range of values in order for the cosmos to develop astrophysical structures and ultimately support life. This paper reviews the current constraints on these quantities. The discussion starts with an assessment of the parameters that are allowed to vary. The standard model of particle physics contains both coupling constants (alpha, alpha(s), alpha(w)) and particle masses (m(u), m(d), m(e)), and the allowed ranges of these parameters are discussed first. We then consider cosmological parameters, including the total energy density of the universe (Omega), the contribution from vacuum energy (rho(Lambda)), the baryon-to-photon ratio (eta), the dark matter contribution (delta), and the amplitude of primordial density fluctuations (Q). These quantities are constrained by the requirements that the universe lives for a sufficiently long time, emerges from the epoch of Big Bang Nucleosynthesis with an acceptable chemical composition, and can successfully produce large scale structures such as galaxies. On smaller scales, stars and planets must be able to form and function. The stars must be sufficiently long-lived, have high enough surface temperatures, and have smaller masses than their host galaxies. The planets must be massive enough to hold onto an atmosphere, yet small enough to remain non-degenerate, and contain enough particles to support a biosphere of sufficient complexity. These requirements place constraints on the gravitational structure constant (alpha(G)), the fine structure constant (alpha), and composite parameters (C-*) that specify nuclear reaction rates. We then consider specific instances of possible fine-tuning in stellar nucleosynthesis, including the triple alpha reaction that produces carbon, the case of unstable deuterium, and the possibility of stable diprotons. For all of the issues outli