純量張量重力理論中重力常數快速振盪在宇宙學上之演化與早期能量密度之限制條件

Abstract

重力常數G的概念在純量張量重力理論中可以被一個和重力有非 最小耦合的純量場所取代。相較於廣義相對論，這個純量場代表著額 外的自由度。藉由一個均勻、均向且有質量的純量場造成G產生週 期性振盪是可能的。在這篇論文中，我們致力於對G的快速振盪給出 限制。首先，我們展示純量場的運動方程式可以被重新改寫成更加簡潔的 式子，並且發現由純量場引致的等效能量密度會分別在下列三個不 同的時期中有不一樣的行為：第一時期，|ΔG/G|~O(1)；第二時期， ΔG≪G; 100H≳ν 以及第三時期，ΔG≪G; 100H<ν。其中 ν是G振盪的頻率；H是宇宙膨脹率。在第一與第二時期時，非最小耦合及宇宙膨脹會對純量場的動力學行為造成重大的影響，使得等效能量密度的耗散率比第三時期時小上許多。當宇宙進入第三時期後，等效能量密度平均上將會正比於a^(-2)或a^(-3)，取決於非最小耦合的型式與強度。為了吻合G的局域實驗以及觀測宇宙學，我們發現可以從純量場的動力學去限制線性與二次非最小耦合模型中G振盪和純量場貢獻出的等效能量密度。我們最後討論這些限制對早期宇宙中的物理帶來的影響。

In the scalar-tensor theory of gravity, the concept of gravitational constant G can be replaced with a scalar field non-minimally coupled to gravity. This turns out to be an additional degree of freedom compared to general relativity and is possible to induce periodic variations (i.e., oscillations) in G by a homogeneous and isotropic massive scalar field. In this thesis, we aim to constrain the rapid oscillation of G. We first show that the equation of motion of the scalar field can be cast into a fairly graceful formula and the dissipation rate of its effective energy density behaves differently in three epochs of cosmic evolution: I. |ΔG/G|~O(1), II. ΔG≪G; 100H≳ν and III. ΔG≪G; 100H<ν , where ν is the frequency of oscillations and H is the cosmic expansion rate. During the Epoch I and Epoch II, the non-minimal coupling and cosmic expansion could lead to non-trivial effects on the dynamics of scalar field, which make the effective energy density dissipate much slower than in the Epoch III. As the universe enters the Epoch III, the effective energy density is in average proportional to a^(-2) or a^(-3) (a is the scale factor), depends on the form and the strength of non-minimal coupling. To be consistent with local experiments on G and the observational cosmology, we find that it is possible to give phenomenological constraints on the effective energy density contributed from G oscillation and the scalar field from the dynamical behavior of the scalar field in both linear and quadratic non-minimal coupling cases. We finally discuss the impact of the constraints on physics in the early universe.