RELATIVISTIC DYNAMICS AND STRUCTURE FORMATION IN A MATTER—DOMINATED FRIEDMANN UNIVERSE

Abstract

Cosmology as the study of the Universe as a whole, addresses questions on its origin and development and among the unresolved problems in cosmology today is the formation and evolution of structures in the Universe. One of the proposed and successful cosmological model and tested experimentally in addressing this problem is the Friedmann model based on the cosmological principle. This thesis explores the fundamental cosmological principle, with a specific focus on the homogeneity and isotropy assumptions inherent in the Friedmann model underpinning the standard model. The cosmological principle says that the Universe is isotropic and homogeneous on large scales. However, current three-dimensional redshift surveys map the Universe depicting inhomogeneities at all cosmic scales contrary to the cosmological principle view that cosmic matter distribution is statistically isotropic and homogeneous at large length scales. Additionally, there has been an ongoing cosmological debate on whether or not the analyses showing fractal clustering is carried using proper treatment of data, most notably a reliable and accurate amount of available statistical data. These galaxy surveys provide limited statistical data depended on our ability to measure distance accurately. The uncertainties associated with cosmic distance measures are huge and unresolved to date while the availability of huge observational data will wait for the next generation of bigger and advanced telescopes. To address this challenge, the research proposed a modified Friedmann model describing relativistic dynamics, structure formation and evolution based on the distribution of luminous matter in the Universe. In the modified model in which the redshift scale factor relation has been modified, it was assumed that there is huge and accurate astronomical data for measured redshift, number density of galaxies counts per solid angle in a given direction and light intensity counts . Interconnections of these three astronomical quantities was found using Einstein Field Equations. Computer simulations of the derived analytical results produced and the results related to structure formation in a matter―dominated modified Friedmann Universe without dark energy. Galaxy formation, evolution and distribution explained with a modified redshift formalism and compared to the standard model predictions. Analysis of the results suggests that the model can account for cosmic acceleration expansion without the need for dark energy. Simulations based on these models have illuminated structure formation and evolution processes of the early Universe running into the future. The 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 majority of cosmic structures 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. There is a distinctive redshift transition around z ≈ 0.9 is observed before the onset of dark―matter―induced accelerated expansion. This transition is proportional to mass matter density and 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.