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Analytical Study on Cosmological Perturbations with Exact Solutions

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Title: Analytical Study on Cosmological Perturbations with Exact Solutions
Other Titles: 厳密解に基づく宇宙揺らぎの解析的研究
Authors: 佐々木, 伸 Browse this author
Issue Date: 25-Mar-2020
Publisher: Hokkaido University
Abstract: We consider the linear perturbation theory on the homogeneous and isotropic spacetime filled with various kinds of perfect fluid matters. In particular, we solve exactly the time evolution equation for the tensor fluctuation, which represents the amplitude of the gravitational waves, and for a massless minimally coupled scalar field, by using the associated third order differential equation for several combinations of background matters. It turns out that the solutions are given by the Weierstrass's elliptic and related functions, denoted by℘(z),ζ(z), and σ(z). We consider physical properties of these solutions. In the first part the problem of propagation of gravitational waves, which is supposed to be generated in the early universe, is considered in the standard cosmological setting and in the setting with a non-standard matter content, which is considered as a effective model of the quintessence. We obtain the explicit expressions for the energy spectrum of the waves and discuss the physical relevance of them. In the second part we consider a pre-inflationary model, where the radiation and the spatial curvature energy density dominates, followed by the de Sitter inflation. The scalar field equation is solved exactly there and consider the problem of the vacuum choice, especially particle creation caused by the difference from the standard Bunch-Davies vacuum is discussed. Furthermore, the vacuum expectation value of the energy density of the quantum field is calculated with the adiabatic regularization procedure. The quantum correction to the cosmological constant as a function of the density parameters is obtained, and it is found that the correction term canges its sign depending on the spatial curvature. Finally we calculated the primordial power spectrum and large scale suppression compared to the scale invariant spectrum is observed for the flat and closed universe, which is consistent with the results of the previous works. On the other hand, it is found that when the curvature is negative and sufficiently large, it can cause a some enhancement in the large scale.
Conffering University: 北海道大学
Degree Report Number: 甲第13908号
Degree Level: 博士
Degree Discipline: 理学
Examination Committee Members: (主査) 教授 鈴木 久男, 教授 小林 達夫, 准教授 中山 隆一, 講師 末廣 一彦
Degree Affiliation: 理学院(宇宙理学専攻)
Type: theses (doctoral)
Appears in Collections:課程博士 (Doctorate by way of Advanced Course) > 理学院(Graduate School of Science)
学位論文 (Theses) > 博士 (理学)

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