Cosmological models of dark energy: theory and observations

We investigated the evolution of the background expansion and the growth rate of the matter density fluctuations in the scalar field $\phi$CDM Ratra-Peebles model. We constrained the model parameter $\alpha$ and the matter density parameter $\Omega_{\rm m}$ using the recent measurements of the growth rate of the matter density fluctuations and baryon acoustic oscillation peak position. In addition, we studied a number of the $\phi$CDM scalar field models in order to determine whether or not it would be possible to discriminate them from the $\Lambda$CDM model using predicted data for the future Dark Energy Spectroscopic Instrument (DESI) observations. For this purpose, we carried out the statistical Bayesian analysis, and computed Bayes coefficients, as well as Akaike and Bayesian information criteria. We found that projected DESI results could provide compelling when comparing most $\phi$CDM models with the $\Lambda$CDM model. We also conducted the MCMC analysis and obtained the constraints on the parameters of the scalar field models, comparing the observational data for: the universe expansion rate, the angular diameter distance and the growth rate function, with the corresponding data generated for the $\Lambda$CDM model. We investigated how well the Chevallier-Polarsky-Linder (CPL) parametrization approximates the various scalar field models. We determined the location of scalar field model in the phase space of the CPL parameters.