Discrepancies in observational data in cosmology with Hubble parameter as an example

The paper considers an actual and currently unsolved problem of modern astronomy and cosmology related to determining the value of the present Hubble parameter 𝐻0, which characterizes the expansion rate of the Universe. There is an unexplained statistically significant discrepancy in the observational data related to the “near Universe” at small redshifts, and to the “far Universe” (the surface of the last scattering). In the introduction to the paper, a large overview of the state of the problem is given (the so-called “Hubble tension” problem). In this paper, modifications of the dark energy equation of state are introduced and investigated, obtained by introducing a nonlinear dependence of the parameter of the equation of state on time, which generalizes modern approaches to explaining the discrepancy in the value of 𝐻0. A number of models are excluded, which gives restrictions on the type of the parameter of the equation of state.