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Excursion Set Theory Application in Large Scale Structure Formation

Kameli, Hamed | 2021

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 54450 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Baghram, Shant; Rahvar, Sohrab
  7. Abstract:
  8. The standard model of cosmology with Cold Dark Matter (CDM) and cosmological constant ΛCDM, Despite its achievement and success, confronts some important open questions and challenges such as Dark Matter (DM) nature, small scale structure challenge, $H_0$ tension and, etc. In this dissertation, we study the formation and growth of Large Scale Structure (LSS) as one of the most important cosmological observables. Then we propose some solutions to these questions and challenges. We use the Excursion Set Theory (EST) to study the LSS and calculate the LSS observable such as first up-crossing of trajectories from density contrast barrier, the number density of DM halos, conditional number density to form more massive halo from smaller ones, and mass assembly history for DM halos. In the standard version of EST, we use Markov random walk to calculate the first up-crossing and other parameters. In this work, we develop the non-Markov extension of EST by considering the cosmological parameter history. This cosmological parameter's history is applied by defining the correlation function of different mass scales and generating the non-Markov trajectories. These trajectories lead us to more physical predictions. We develop the correlation function for arbitrary and complicated power spectrum in the standard model for the first time. We use the power spectrum with BBKS growth function and Eisenstein-Hu transfer function. Furthermore, We extend the spherical collapse model in the standard version of EST to the ellipsoidal collapse model for DM halos. We develop a Python code to calculate all EST equations, numerical schemes, and algorithms. Finally, we use the developed tool in the following studies.(a) We study the effect of modification in early time cosmological perturbation in curvature power spectrum with a Gaussian bump shape on DM halo number density. We show that the initial power spectrum enhancement leads to significant and non-trivial reduction of DM halos number. This reduction occurs in smaller masses than the power enhancement mass scale. We propose that this modification could solve or diminish the tension of the Missing Satellite (MS) and Too Big to Fail (TBTF) problems. (b) We study the possibility that Primordial Black Holes (PBHs) form all or part of DM by enhancing the initial curvature power spectrum. We apply the enhancement by using a blue-tilted spectral index. We calculate the required spectral index to generate all DM from Primordial Black Hole (PBH) in different mass ranges. Also, we calculate the spectral index for constrained mass range. (c) We study the effect of Hubble parameter deviation (reconstructed Hubble parameter) based on late time local observation on the LSS observable. We show that the DM halo number density and mass assembly history are different by almost $\sim 2\sigma$ in the reconstructed and standard model. Also, we propose that by increasing five times the accuracy of observations of pair galaxies and comparison of calculation with observation, it is possible to distinguish between the reconstructed and standard models
  9. Keywords:
  10. Excursion Set Theory ; Dark Matter Halo ; Primordial Black Holes ; Large Scale Structure ; Small Scale Challenge ; Missing Satellite ; Cold Dark Matter ; Hubble Constant Stress

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