Early and late time cosmology in theories of modified gravity

宇宙学数据与宇宙具有封闭几何结构是一致的。如果是这样的话，宇宙可能会在未来停止膨胀，收缩、反弹并随后再次膨胀，而不需要宇宙从大爆炸开始。在这个项目中，这些场景是在爱因斯坦引力理论的扩展中进行研究的。在最初的部分，将使用各种理论来构建模型，例如标量-张量或f(R)理论。将采用多种方法来研究场方程的解，包括动力系统分析和数值模拟。它还可能要求学生分别研究晚期和早期的宇宙学。一旦找到一致的解，将进行稳定性分析，以查看曲率扰动是否保持小(和有限)。这就需要深入研究宇宙微扰在塌缩和反弹背景时空中的传播。该项目的另一个目标是研究爱因斯坦理论的扩展，该理论允许暗能量衰减，使曲率决定随后的动力学。该项目将产生新颖的宇宙学场景，这些场景将在未来十年内进行的宇宙学观测中得到检验。

Cosmological data are consistent with the universe having a closed geometry. If this is the case, the universe could stop expanding in the future and contract, bounce and subsequently expand again, without the universe having to begin with a big bang. In this project, such scenarios are investigated in extensions of Einstein's theory of gravity. In the initial part, models will be constructed in various theories such as scalar--tensor or f(R) theories. A variety of methods to study the solutions of the field equations will be employed, including dynamical system analysis and numerical simulation. It will also probably require the student to study the late and early time cosmologies separately. Once consistent solutions have been found, a stability analysis will be performed to see whether the curvature perturbations remain small (and finite). This requires an in-depth study of cosmological perturbations propagating on the collapsing and bouncing background spacetime. Another aim of the project is to study extensions of Einstein's theory, which allow dark energy to decay such that curvature determines the subsequent dynamics. This project will lead to novel cosmological scenarios which will be tested with future cosmological observations available within the next decade.