Abstract
An overview of the problems associated with the possible going beyond the basic cosmological model is given. The focus is mainly on issues related to astronomical observations and the modifications of general relativity, which use a cosmological scalar field or nonlinear in curvature terms in gravitational Lagrangian. The main points are as follows: the problems of flatness and horison, discussion of the “Hubble Tension” and the simplest known models with one scalar field and the modified gravity. The general opinion is that that there is a number of ways to solve problems with the Hubble constant, but none of them explains all the completeness of the observational data. They are either phenomenological in nature or contain arbitrary functions that must be determined from experiment or from some fundamental principles. Therefore, it is natural to first turn to those models that either do not introduce “new entities”, or include a minimum number of new physical elements and a minimum number of additional parameters.
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