Study On Microwave Background Fluctuations And Large Scale Structures In Non-Thermal Production Of Dark Matter Model

In the past decade, especially from 2003, the high-resolution observations of the cosmic microwave background by the Wilkinson Microwave Anisotropy Probe (WMAP) satellite and the massive statistical surveys of galaxies and large-scale structure by the Sloan Digital Sky Survey (SDSS), combined with the observations by the distant supernovae (SN), have marked a new epoch of "precision cosmology" and allowed us to constrain essentially all of the cosmological parameters. The dark energy dominated cold dark matter (CDM) scenario with scale invariant primary power spectrum has been a standard model for cosmology, i. e. ACDM model.Now, the research on cosmology focus on dark matter, microwave background fluctuation and large scale structures, which has significance to understand the distribution and evolution of cosmic matter. Different dark matter models result in defferent microwave background fluctuations, and affect the formation and evolution of large-scale structures. Although the ACDM model can explain the formation and evolution of large scale structures, it conflict with the astronomical/cosmological observations on small scales.The purpose of the PhD thesis is to construct a standard model for cosmology based on dark matter, whose predictions are in agreement well with the observations. Thus, I study the dark matter, the evolution of the cosmic matter, and formation and evolution of large scale structures.The first chapter is to introduce the relevant background of cosmology, including standard model of cosmology, theory of structure formation, and bases and properties of dark matter. And we introduce the dark matter halo model and the methodology of research on halo.In Chapter 2, we present a systematic treatment of the linear theory of scale gravitation perturbation of various matters (including baryons, cold dark matter, photons, massless neutrinos, and massive neutrinos) for expanding universe, and obtain the evolution equations for matter and radiation. Our results can be served as the basis, on which one can calculate the linear transform functions of matter perturbation in various cosmic models and calculate the accurate angular power spectrum of the CMB. We also give the accurate calculations of the angular power spectra.In Chapter 3, we introduce the ACDM model based on WIMP dark matter and give the standard calculations of relic abundance of the thermal produced dark matter. Then we analyze the success of the model to explain the formation an evolution of large scale structures, although there still are some challenges on small scale, e.g., sub-structure problem, and density profile problem, referred as small-scale crisis.Then we present the alternative model base on non-thermal production of WIMP dark matter to solve the small-scale problems. The WIMP dark matter is produced by the decay of cosmic strings which form at a phase transitions associated with the spontaneous symmetry breaking, which is referred as NTDM. In the second part of Chapter 3, we detail the non-thermal production mechanism, and present the calculations of the relic abundance of NTDM particles. Moreover, combined the astronomical/cosmological observations, we give constrains on the symmetry breaking scale.In the third part of Chapter 3, we present the evolution equations for NTDM by using the methodology detailed in Chapter 2. And we obtain results of the numerical calculations, including linear transform function, the linear matter power spectrum and the angular power spectrum of the CMB, by modifying the numerical program CMBFAST. Moreover, comparing with the SDSS main-galaxy 3D power spectrum, the NTDM model can explain the large scale structures reasonably. Combined with the Lyman-a forest data, we present constrains on the NTDM particle and exclude the possibility of over-light particle as the candidate for dark matter. We construct the cosmology model based on the NTDM, assuming a scale-invariant, adiabatic spectrum of primordial fluctuation, i.e. ANTDM model.In Chapter 4, using the high-solution simulations, in the ANTDM model, we explore the nonlinear evolution of cosmological structures, and give the distribution of dark matter, and analyze the statistical properties of dark matter. The application of the simulation of dark matter is to study the distribution of halo and the interior non-linear structure. We present the halo model using the spherical over-density algorithm, and give mass functions and the density profiles of halo, and analyze the evolution of the power spectra of halo, and evolution of the number density of various mass halos, and the shape of halo.At the same time, we conduct the simulations in ACDM model to compare the results of various cosmology models. The ANTDM model can explain the formation and evolution of large scale structures, and can solve the small-scale crisis.The last chapter is to conclude with summarization of the main results and innovations, and especially to direct the further study.