This work discusses the Friedmann equations, which govern the accelerated expansion of the Universe. A crucial role in this process is played by the scale factora(t). The universe consists of multiple components, each possessing a distinct pressure-density relationship (equation of state), which consequently affects the evolution of the scale factor. After analyzing cosmological quantities and distances, as well as phenomena such as the Cosmic Microwave Background (CMB), Baryon Acoustic Oscillations (BAO), and Type Ia Supernovae (SNIa)—which provide valuable information regarding cosmic expansion—an extensive analysis using maximum likelihood estimation is conducted to determine the best-fit parameters. Furthermore, various cosmological models are presented as alternatives to address the unresolved issues associated with the ΛCDM model. Finally, by utilizing observational data and the χ² function, a comparison of these models is performedand the evolution of the scale factor according to the preferred model is designed, providing an overview of the parameter correlations depending on the specific model and the datasets employed.