This paper explores the fundamental cosmological principle, with a specific focus on the homogeneity and isotropy assumptions inherent in the Friedmann model that underpins the standard model. We propose a modified redshift model that is based on the spatial distribution of luminous matter, examining three key astronomical quantities: light intensity, number density, and the redshift of galaxies. Our analysis suggests that the model can account for cosmic accelerated expansion without the need for dark energy in the equations. Both simulations and analytical solutions reveal a unique pattern in the formation and evolution of cosmic structures, particularly in galaxy formation. This pattern shows a significant burst of activity between redshifts 0 < z < 0.4, which then progresses rapidly until approximately z ≈ 0.9, indicating that the majority of cosmic structures were formed during this period. Subsequently, the process slows down considerably, reaching a nearly constant rate until around z ≈ 1.6, after which a gradual decline begins. We also observe a distinctive redshift transition around z ≈ 0.9 before the onset of dark-matter-induced accelerated expansion. This transition is directly related to the matter density and is dependent on the geometry of the universe. The model’s ability to explain cosmic acceleration without requiring fine tuning of the cosmological constant highlights its novelty, providing a fresh perspective on the dynamic evolution of the universe.

In this paper, we examine a modified Friedmann model designed to explain cosmic structures and late-time accelerated expansion of the universe, grounded in the spatial distribution of luminous matter. Through comprehensive simulations of our universe, we observe a notable surge in the formation rate of galaxies at redshift z≈1, characterized by a peak expansion rate in cosmic structures formed at z ≈0.9, reaching its zenith at z ≈2. Subsequently, a transition occurs before the onset of dark matter-induced accelerated expansion. The acceleration of the universe stands as an entrenched and virtually model-independent theoretical tenet, resilient to the ongoing debate surrounding the enigma of dark energy. A distinctive redshift transition zone marks the shift from cosmic deceleration to accelerated expansion. The transition is proportional to matter density and contingent upon the geometry of the universe. The influence of the cosmological constant on the evolution of cosmic structures in the CDM paradigm appears insufficient in curtailing the efficiency of late-time structure formation compared to the observed values in the modified model