Flat cosmology with collisionless cold dark matter (CDM) and cosmological constant ([Lambda]CDM cosmology) may have some problems on small scales, even though it has been very successful on large scales. We study the effect of Self-Interacting Dark Matter (SIDM) hypothesis on the density profiles of halos. Collisionless CDM predicts cuspy density profiles toward the center, while observations of low mass galaxies prefer cored profiles. SIDM was proposed by Spergel & Steinhardt [161] as a possible solution to this cuspy profile problem on low-mass scales. On the other hand, observations and collisionless CDM agree on mass scales of galaxy clusters. It is also known that the SIDM hypothesis would contradict with X-ray and gravitational lensing observations of cluster of galaxies, if the cross section were too large. Our final goal is to find the range of SIDM scattering cross section models that are consistent with those astrophysical observations in two different mass scales. There are two theoretical approaches to compute the effect of self-interacting scattering -- Gravitational N-body simulation with Monte Carlo scattering and conducting fluid model; those two approaches, however, had not been confirmed to agree with each other. We first show that two methods are in reasonable agreement with each other for both isolated halos and for halos with realistic mass assembly history in an expanding [Lambda]CDM universe; the value of cross section necessary to have a maximally relaxed low-density core in [Lambda]CDM is in mutual agreement. We then develop a semianalytic model that predicts the time evolution of SIDM halo. Our semianalytic relaxation model enables us to understand how a SIDM halo would relax to a cored profile, and obtain an ensemble of SIDM halos from collisionless simulations with reasonable computational resources. We apply the semianalytic relaxation model to CDM halos, and compare the resulting statistical distribution of SIDM halos with astrophysical observations. We show that there exists a range of scattering cross sections that simultaneously solve the cuspy core problem on low-mass scales and satisfy the galaxy cluster observations. We also present that other potential conflicts between [Lambda]CDM and observations could be resolved in Part II and III. / text

This thesis investigates the possibility that the gauge boson in a certain hypothetical SU(2) gauged sector can constitute all the non-baryonic dark matter. The gauge bosons acquire mass from the Higgs mechanism as in the Standard Model and scatter elastically among themselves non-gravitationally. It is expected that this self interaction of the dark gauge bosons would resolve the various discrepancies between the ΛCDM model and astrophysical observations on small (e.g. galactic or galaxy cluster) scales. Parameter space within the domain of validity of perturbation theory satisfying the constraints of dark matter abundance, the elastic self-scattering momentum transfer cross-section suggested by recent astrophysical observations, and consideration of the Big-Bang nucleosynthesis was found to be non-empty in the “forbidden” regime where the mass of the dark Higgs boson is greater than the mass of the dark gauge boson. / Graduate

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