LCS 理論的穩定性分析和 WKK 理論

Abstract

In this thesis, we will discuss two models of modified gravity. The first one is the Lorentz Chern-Simons gravity. We will analyze the LCS gravity in FRW space, Bianchi I space and Bianchi II space. In the sector of FRW space, we will try to compare our solutions with the solutions of Standard-model Cosmology to see whether LCS gravity could be a good candidate of modified gravity. In the sector of Bianchi I space, we will show that the solutions we find are indeed the perfect examples of cosmic no-hair theorem. We will also analyze the stabilities of our solutions. In the sector of Bianchi II space, we reproduce the solutions found by Kaloper. We will also analyze the stabilities to verify whether Kaloper's solutions are the counterexamples of no-hair theorem. The second model we will discuss is the Weyl-invariant Kaluza-Klein theory. Literally, we integrate both Weyl gravity and Kaluza-Klein theory to form a new modified gravity. We will first demonstrate how to construct the Weyl-invariant Kaluza-Klein theory step by step. We then show the Teleparallel equivalence of Weyl-invariant general relativity is also true and will reduce to the Teleparallel equivalence of general relativity. Finally, we analyze the Cosmology of Weyl General Relativity in de Sitter space and Bianchi I space. In the sector of de Sitter space, we will compare the solutions of de Sitter space with the solutions of Standard-model Cosmology again. In the sector of Bianchi I space, we demonstrate the anisotropic solutions we find and analyze the stabilities of these solutions.