| The accelerating expansion of the universe is considered to be a well-established fact. However, a physical explanation of its origin is still missing. While the cosmological constant, Lambda, is the favorite candidate, a multitude of other theories have been proposed. Rather than testing every theory against data, one can adapt phenomenological approaches aimed at testing Lambda.;Adopting a model-independent approach to studying dark energy, we have investigated the utility of wavelets for constraining the redshift evolution of the dark energy equation of state, w(z), from a combination of the type Ia supernovae (SNe Ia), cosmic microwave background (CMB) and baryon acoustic oscillation (BAO) data. We have shown that sharp deviations from wLambda = -1 can be detected efficiently. Applying this method to the "Constitution" SNe Ia data, combined with the CMB data from Wilkinson microwave anisotropy probe (WMAP) and BAO data from Sloan digital sky survey, provided only weak hints of dark energy dynamics.;Future weak lensing surveys will have the ability to measure the growth of large scale structure with accuracy sufficient for discriminating between different theories of dark energy and modified gravity (MG). The growth of structure can be tested, in a modelindependent way, by parametrizing the evolution equations of cosmological perturbations. At the linear level, this can be achieved by introducing two scale- and time-dependent functions (MG functions). We have consistently implemented the parametrized equations in the commonly used public codes, CAMB and CosmoMC, while preserving the covariant conservation of the energy-momentum. As a demonstration, we have obtained joint constraints on the neutrino mass and parameters of a scalar-tensor gravity model from the CMB, SNe Ia and the correlation of CMB with large scale structure.;We have performed a Principal Component Analysis (PCA) to find the eigenmodes and eigenvalues of the forecasted covariance matrix of the MG functions for surveys like Dark Energy Survey and Large Synoptic Survey Telescope. By examining the eigenmodes, we can learn about the scales and redshifts where the surveys are most sensitive to modification of the growth. We have considered the impact of some of the systematic effects expected in weak lensing surveys. Also, we have demonstrated the utility of the PCA as an efficient way of storing information about the linear growth of perturbations.;Finally, we have analyzed the degeneracy between the MG functions and other cosmological parameters, paying special attention to the effective equation of state w(z). We have taken several models with different MG parametrizations and studied their merits. We have shown how the complementarity of different observables helps break the degeneracies.;Key words: dark energy, modified gravity, cosmological parameters, observational constraints, principal component analysis, massive neutrinos. |
