Early and late time cosmology in theories of modified gravity

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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.