Quintessence cosmology and the cosmic coincidence

Abstract

Within present constraints on the observed smooth energy and its equation of state parameter ${w}_{Q}=P/{\ensuremath{\rho}}_{Q},$ it is important to find out whether the smooth energy is static (cosmological constant) or dynamic (quintessence). The most dynamical quintessence fields observationally allowed are now still fast rolling and no longer satisfy the tracker approximation if the equation of state parameter varies moderately with cosmic scale $a=1/1+z.$ We are optimistic about distinguishing between a cosmological constant and appreciably dynamic quintessence by measuring average values for the effective equation of state parameter ${w}_{Q}(a).$ However, reconstructing the quintessence potential from observations of any scale dependence ${w}_{Q}(a)$ appears problematic in the near future. For our flat universe, at present dominated by smooth energy in the form of either a cosmological constant (LCDM) or quintessence (QCDM), we calculate the asymptotic collapsed mass fraction to be maximal at the observed smooth energy-matter ratio ${\mathcal{R}}_{0}\ensuremath{\sim}2.$ Identifying this collapsed fraction as a conditional probability for habitable galaxies, we infer that the prior distribution is flat in ${\mathcal{R}}_{0}$ or ${\ensuremath{\Omega}}_{m0}.$ Interpreting this prior as a distribution over theories, rather than as a distribution over unobservable subuniverses, leads us to heuristic predictions about the class of future quasistatic quintessence potentials.