Abstract
In the framework of Barrow and Tsallis entropy corrected cosmologies, we investigate the growth of matter perturbation for zero spatial curvature Friedmann–Robertson–Walker metric. These entropy changes add additional parameters to the Friedmann equations, which have the potential to have a major impact on expansion history and development of cosmos structure. For matter density contrast [Formula: see text], we examine the evolution equation and examine the growth rate function [Formula: see text] for the Barrow and Tsallis entropy corrections. We observe the effects of these entropy adjustments on the comoving number density of galaxy clusters. We compare conventional [Formula: see text]CDM model with comparison graphs of matter density contrast, growth rate function and number of galaxy clusters for different values of the entropy parameters and found interesting results.