Analyzing cosmic inhomogeneities through perturbative modifications of FLRW spacetime

Abstract This research study investigates the modification of Friedmann–Lemaitre–Robertson–Walker (FLRW) spacetime, emphasizing the effects of universe expansion, dark matter, and cosmological perturbations. The study explores the interplay of dark matter in modifying gravitational forces and its role in sustaining galaxy structures. We insert spatial perturbation into FLRW spacetime by using the Noether symmetry equation. This type of spatial perturbation is considered to study the inhomogeneous nature of the universe. On the other hand the dark matter and dark energy also deviate the trajectories of the spacetime leaving a room for spatial perturbation. The spatial perturbation is introduced in a manner that preserves the symmetric structure of the FLRW spacetime. We study different dynamical aspects of the perturbed FLRW spacetime. Graphical analyses reveal the impact of modifications on gravitational behavior, expansion rates and particle motion, offering theoretical alignments with dark matter, dark energy, quantum gravity and higher-dimensional models. This study enhances the understanding of cosmic expansion, dark matter and the universe evolution.