f(R) Gravity and Spherical Collapse

This thesis studies f(R) model building, cosmological dynamics, Solar System tests of f(R) gravity, and spherical collapse in f(R) gravity. We apply the running coupling idea to gravity. We describe several well-known f(R) models in a simple way in terms of infrared renormalization group flow. We explore two logarithmic models, produced by the flows. These two models generate a large hierarchy between the Planck scale and the cosmological constant scale. We study the cosmological dynamics of a range of f(R) models, presenting generic features of phase-space dynamics in f(R) cosmology. New techniques to explore phase space dynamics are developed. These techniques are very general and can be applied to other similar dynamical systems. We investigate the Solar System tests of f(R) gravity. The metric is rederived by directly focusing on the equations of motion. The chameleon mechanism in the Jordan frame is considered. These approaches provide a more intuitive understanding of the Solar System tests of f(R) gravity. We explore spherical scalar collapse in f(R) gravity numerically. We study the dynamics throughout the collapse. Mesh refinement and asymptotic analysis are implemented in the vicinity of the singularity of the formed black hole. The Kasner solution for spherical scalar collapse in f(R) gravity is obtained. These results support the Belinskii-Khalatnikov-Lifshitz conjecture well in the context of black hole physics.