**Bulletin of Taras Shevchenko National University of Kyiv. Astronomy, no. 61, p. 22-25 (2020)**

**Hubble parameter in f(R)-gravity**

**V. Zhdanov, Dr Hab.**

**O. Stashko, PhD Student**

**Taras Shevchenko National University of Kyiv **

**Abstract**

In view of the famous problem with the “Hubble constant tension” there is a number of approaches to modify the cosmological equations and correspondingly modify Hubble parameter H(z) in order to to relieve the tension between the “early” and “late” Hubble constants. f(R)– gravity is one of such possible modifications. We discuss how to choose the Lagrangian in the f(R)– gravity on account of observational data within the homogeneous isotropic cosmology. The equation is obtained that enable us to derive f(R) for given Hubble parameter H(z). This yields a second order differential equation with corresponding degrees of freedom. If H(z) corresponds to that obtained from usual Friedmann equations, this equation yields a condition for f(R) to mimic the observable quantities of the standard ΛCDM with the above-mentioned freedom. To reduce this freedom on needs additional considerations, which involve the other observable quantities, such as those which appear in considerations of cosmological perturbations on the isotropic and homogeneous background. Also, we consider the reverse problem to find for given f(R). This is fulfilled within an approximation in case of small deviation of f(R) from the General Relativity value.

**Key words
**Cosmology, Hubble parameter, f(R)-gravity.

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