In deep three­dimensional surveys of galaxies, as the third coordinate of a galaxy's position in space its redshift is adopted. Density inhomogeneities in the Universe induce deviations from the simple Hubble velocity flow of galaxies. As a result, redshift is not a perfect estimator of the true distance and maps of the galaxy distribution in REDSHIFT SPACE give a distorted view of their spatial distribution in real (configuration) space. In particular, the two­point (auto­)correlation function of galaxies is anisotropic in redshift space. Interestingly, the amount of anisotropy depends on the rate of growth of density fluctuations in the Universe, which is different in dark energy and modified gravity cosmologies. A measurement of the growth rate from galaxy redshift surveys can thus serve as a method to differentiate between various competing cosmological theories, explaining the current acceleration of the Universe expansion in a qualitatively distinct way.

To achieve this goal, very accurate estimates of the growth rate from observations, as well as precise theoretical models of the correlation function of galaxies in redshift space are needed. The accuracy of the measurements steadily increases with time. However, despite of numerous attempts over the last two decades, there is still no model which satisfactorily predicts isocontours of the correlation function in redshift space. After describing a few most popular models existing in the literature, I will briefly present my recent work on the subject. My model has more realistic physical assumptions and in consequence fares much better than the former when compared to the results of N­body simulations.