Applying Friedmann models to describe the evolution of the Universe based on data from the SAI Supernovae Catalog

In the recent years thanks to the modern and sophisticated technologies the astronomers and astrophysicists were able to look deep into the Universe. This vast data poses some new problem to the cosmologists. One of the problems is to develop an adequate theory. Another one is to fit the theoretical results with the observational one. In this report within the scope of the isotropic and homogeneous Friedman-Lemaitre-Robertson-Walker (FLRW) cosmological model we study the evolution of the Universe filled with dust or cosmological constant. The reason to consider this model is the present universe surprisingly homogeneous and isotropic in large scale. We also compare our results with the data from the SAI Supernovae Catalog. Since the observational data are given in terms of Hubble constant (????) and redshift (????) we rewrite the corresponding equations as a functions of ????. The task is to find the set of parameters for the mathematical model of an isotropic and homogeneous Universe that fits best with the astronomical data obtained from the study of supernovae: magnitude (????), redshift (????).