| Summary: | This thesis studies the viability of classes of modified gravity (MG) theories based on generalisations of the Einstein-Hilbert action. Particular emphasis is given to f(R) theories in both the metric and Palatini formalisms, scalar-tensor theories and generalised Gauss-Bonnet theories. An urgent task at present is to devise stringent tests in order to reduce the range of candidate models based on these theories. In this thesis a detailed study is made of the viability of these models using constraints from requirement of stability, background cosmological dynamics, local gravity constraints (LGC) and matter density perturbations. In each case the conditions required for stability and viability of the background dynamics are presented. In the case of generalised Gauss-Bonnet theories the circumstances leading to the existence and stability of cosmological scaling solutions are established. In the scalar-tensor theories considered here, which includes metric-f(R) theories as a special case, there is a strong coupling of the scalar field to matter in the Einstein frame which violates all LGC. It is shown that using a chameleon mechanism, models that are compatible with LGC may be constructed. It is found that such models, which are also consistent with background dynamics, are constrained to be close to the CDMmodel during the radiation/matter epochs and can lead to the divergence of the equation of state of dark energy. In contrast, such constraints only impose mild restrictions on Palatini-f(R) models. Still more stringent constraints are provided by studying matter density perturbations. In particular, it is shown that the unconventional evolution of perturbations in the Palatini formalism leads to f(R) models in this case to be practically identical to the CDM model. For each case it is also shown that (for viable models) matter perturbation equations derived under a sub-horizon approximation are reliable even for super-Hubble scales provided the oscillating mode does not dominate over the matter-induced mode. Such approximate equations are especially reliable in the Palatini formalism, where the oscillating mode is absent. In summary, the analyses carried out in this thesis suggest that subjectingMG theories to observational constraints confines the viable range of models to be very close to (and in some cases indistinguishable from) the CDM model.
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