The cosmological relic density of the lightest supersymmetric particle of the minimal supersymmetric standard model is calculated under the assumption of gauge and Yukawa coupling unification. We employ radiative electroweak breaking with universal boundary conditions from gravity-mediated supersymmetry breaking. Coannihilation of the lightest supersymmetric particle, which turns out to be an almost pure B-ino, with the next-to-lightest supersymmetric particle (the lightest stau) is crucial for reducing its relic density to an acceptable level. Agreement with the mixed or the pure cold (in the presence of a nonzero cosmological constant) dark matter scenarios for large scale structure formation in the universe requires that the lightest stau mass is about $2-8\%$ larger than the B-ino mass, which can be as low as 222 GeV. The smallest allowed value of the lightest stau mass turns out to be about 232 GeV.

The generation of a kination-dominated phase by a quintessential exponential model is investigated and the parameters of the model are restricted so that a number of observational constraints (originating from nucleosynthesis, the present acceleration of the universe and the dark-energy-density parameter) are satisfied. The decoupling of a thermal cold dark matter particle during the period of kination is analyzed, the relic density is calculated both numerically and semi-analytically and the results are compared with each other. It is argued that the enhancement, with respect to the standard paradigm, of the cold dark matter abundance can be expressed as a function of the quintessential density parameter at the onset of nucleosynthesis. We find that values of the latter quantity close to its upper bound require the thermal-averaged cross section times the velocity of the cold relic to be almost three orders of magnitude larger than this needed in the standard scenario so as compatibility with the cold dark matter constraint is achieved.