Abstract
This paper explores the phenomenon of gravitational redshift within the framework of extended gravity models, which go beyond the conventional Einsteinian General Relativity. We establish a relationship between the redshift and the normalized scale factor of the universe, linking it through the Hubble parameter .We develop both analytical and numerical approaches to examine the time evolution of redshift. By solving the governing equations, we derive expressions for , and their derivatives with respect to time. The results align with current cosmological observations and provide new insights into the dynamics of the universe’s expansion. Additionally, visualizations of the evolution of the scale factor, its first and second derivatives over time are presented. These findings contribute to a better understanding of the complex interaction between gravitational forces and cosmic expansion.