TOPICS IN COSMOLOGY: STRUCTURE FORMATION, DARK ENERGY AND RECOMBINATION BY

The field of theoretical cosmology consists of numerous, inter-related branches, whose ambitious goal is to uncover the history of the universe from its beginning to its future. Achieving this, no doubt, requires a deep understanding of many areas of physics. In this thesis I touch upon a few of these areas in which I worked during my PhD studies. Chapter (2) describes our work in finding the accretion and merger history of dark matter halos. Dark matter halos are the collapsed dark matter structures in the late time evolution of the universe, whose existence is vital for the formation of galaxies in the Universe as they act as the potential wells where normal matter (collectively called Baryons) can accumulate, cool, and form stars. It is then no surprise that the properties of galaxies depends on the properties of the dark matter halo in which it resides, including its merger history, i.e. the number of times it merged with other halos. Even though these merger rates can be calculated theoretically for infinitesimal time steps, in order to find the merger history over an extended period of time one had to use either Monte-Carlo simulations to build up the total rates of merging and accreting from the infinitesimal rates or use N-body simulations. In chapter (2) we show how we used random walk formalism to write down an analytical (integral) equation for the merger history of halos. W