Dynamics of the Homogeneous, Isotropic Universe: Metric, Perturbations, Lyman-alpha Forest and Fourier Transform Applications

Beginning with an examination of the fundamental metric for such a universe, known as the Robertson-Walker metric, the paper dives into the concept of proper distance, which plays a crucial role in understanding the cosmic scale.

The study then proceeds to delve into the equations governing the expansion of the universe, providing insights into the forces and factors that contribute to its evolution. Cosmological perturbation theory is introduced as a framework for studying small fluctuations in the cosmic fluid, considering both static and expanding space scenarios and highlighting the significance of gravity in shaping the structure of the universe.

A significant portion of the paper is dedicated to investigating the Lyman-alpha forest, a powerful tool used in studying the intergalactic medium. The methods and techniques employed to analyze this phenomenon are discussed, with a particular emphasis on the Gunn-Peterson trough—an absorption feature observed in the spectra of distant quasars.

Furthermore, the paper explores the Fourier transform and its applications in cosmology. Starting with basic definitions, it covers concepts such as convolution and the discrete Fourier transform. The relevance of these mathematical tools in the analysis of cosmological data is emphasized, demonstrating their utility in extracting valuable insights from observational data.

Also, I explored a bit further and added something extra in Codes directory to supplement the theoretical discussions with practical implementations using the FFTW library. I've added some Python codes to plot interesting Cosmological curves.