大尺度重力場結構

Abstract

大尺度重立場不是需要暗物質就是需要替代理論，而且很有可能，這兩個方向 其實是一體兩面：替代理論其實是暗物質的collective effect．所以這一個議題 的確認，關係到未來宇宙學與天文學發展的關鍵．尤其最近包括我們在內對相對論 性替代理論的研究不但有長足進展，有興趣的研究人員激增． 大尺度重力場可能的替代理論與其背後真正的原因，需要在真實的模型上加以 探討．目前星系質量分佈的量測，相當依賴間接的理論支援，我們最近的論文已經 將盤面分佈質量系統的數學工具加以改良，使得很多以往無法進行分析的工作得以 精確評估．因此，我們將利用本身對數學工具掌握的優勢，更細緻地探討替代理論 背後共同保有也最重要的原始面貌． 我們將專注各種相對性替代理論的分析與比較，並加強這些模型的應用與影響 的研究上．原先可能遇到分析上的困難，我們發展出來的新方法〔參考資料１０〕， 將原先無法順利預估的各種性質，變成可行．我們將積極應用這些工具於螺旋星系 相關研究與宇宙演化等大尺度物理的研究上．

Physics beyond the scale of the order 105 pc, a typical size of any galaxy, appears to take a different form as compared to the familiar Newtonian dynamics. One is looking for a best way to resolve this problem. MOND as an alternative theory proposed by Milgrom could be explained solely by the in-homogeneity of scalar field shown in Ref. [8]. This could be a minimum way to accommodate the large scale spatial distortion of the Newtonian dynamics. The paper only shows that it is possible to reproduce required dynamics deformation, whatever form it may takes, with the coupled mass-deformation scalar field ψobey a special constraint, ψV0 =ΦV. One does not know the physical origin of this constraint. Even this is a big step toward the realization of the physical origin of the alternative theory, there are more to be done. Therefore, we propose to study and compare all possible candidates of the alternative theory including the models with dark matter as part of its constituents. Extending of this study to a spiral system will require a detailed knowledge on the disk-like mass distribution. Most of the mathematical tools rely heavily on an elaborate application of Bessel functions and elliptic functions. Useful formulae regarding these functions have been set up by Toomre [9]. We have succeeded in improving related formulae and make the analytic and numerical analysis more accessible [10]. Therefore, it should be easier for us to extend our current research activity further toward a more realistic frontier. Hence one will generalize our current result further and try to realize possible links between all possible resolutions to the alternative theory. Especially, one would like to see how successful models in cosmology have to do with the theory of MOND.