A new bound dark energy , BDE , cosmology has been proposed where the dark energy is the binding energy between light meson fields that condense a few tens of years after the big bang . It is reported that the correct dark energy density emerges using particle physics without fine tuning . This alone makes the BDE cosmology worthy of further investigation . This work looks at the late time BDE predictions of the evolution of cosmological parameters and the values of fundamental constants to determine whether the cosmology ’ s predictions are consistent with observation . The work considers the time period between a scale factor of 0.1 and 1.0 . A model BDE cosmology is considered with current day values of the cosmological parameters well within the observational limits . The calculations use three different values of the current day dark energy equation of state close to minus one . All three cases produce evolutions of the cosmological parameters and fundamental constants consistent with the observational constraints . Analytic relations between the BDE and cosmological parameters are developed to insure a consistent set of parameters .