Predictive relations between the merging history of galaxies and topologically flat cosmological models
Understanding the merger rate history of galaxies is critical to understanding the formation, structure, and evolution of galaxies. Moreover, the sensitivity of the galaxy merger rate to the cosmological environment enables mutual constraints to be formulated between these two major scientific quandaries. In this dissertation, we have modeled the connection between galaxy merger rates and topologically flat cosmologies with varying multi-component energy density parameters---matter (ΩM), radiation (ΩR), cosmic strings (Ω S) and dark energy (ΩX). We performed kinematic tests deriving look back times, scale factors, deceleration parameters, proper distances, luminosity distances, angular diameter distances and comoving volume elements as a function of redshift (z). We found that models with greater Ω X (less ΩS) and more negative values of the dark energy parameter (w or α) provide greater values of the cosmological age H oto in fixed ΩM. Moreover, we found that the models with greater Hoto provide greater cosmological distances and comoving volume elements. The merger rate is often expressed as a power law of the redshift z, where the exponent m varies from 2 to 7 according to many observational and theoretical studies. We model the merger rate in terms of the number of interacting galaxies N, the dark energy parameter w (or α), the merger rate exponent m, and other cosmological parameters---where a flat topology is assumed. We find that m and α (or w) mutually constrain one another with unique dependences on particular cosmologies. Consequences of these variations on the number of galaxy mergers are plotted on Normalized Three Dimensional (N3D) plots. Forthcoming observations of the Universe's expansion history will help to further constrain α (or w), m, and other parameters (ΩX, ΩS and Ω M) relating to the structure, content, and evolution of the Universe. The inclusion of the cosmic string component, ΩS, in our calculation lays the groundwork for future tests of models with a significant cosmic string contribution.