Dark Energy and Growth of Structure in Modified-Gravity Theories

The past two decades have witnessed the emergence and flourishing of precision cosmology. Vast amount of high-quality observational data, especially those of the large scale structure and the cosmic microwave background, have been taken and analyzed. Rich information of the history, composition and structure of the Universe is still to be mined from them. Higher resolution surveys, larger coverage of the sky, better modeling of systematics, incorporation of more mature statistical and numerical tools --- all of those have laid the foundation for a data-driven investigation of fundamental questions, in particular the crucial one of dark energy. What gives rise to the late-time accelerated expansion of the Universe? In this dissertation, we investigate different ways to make use of the present very-rich observational resources to probe proposed dark energy models and modifications to general relativity that incorporate a late-time cosmic acceleration. We first present a quantitative study of the question: if modifications to general relativity are (mis-)interpreted as a phenomenological dark energy model, how will this bias our cosmological analysis results? We develop, for the first time to our knowledge, a quantitative schematic to address this question and find that modified gravity models masquerading as standard gravity can lead to very specific biases in standard-parameter spaces. In the next study, we present evidence showing that growth of structure is suppressed at late times. Constraining the "growth index" that parameterizes the linear growth rate of matter density perturbations with the cosmic microwave background data from Planck and the large-scale structure data from weak lensing, galaxy clustering, and cosmic velocities, we find that data favor a value of growth index that is 3.7-sigma higher than the 0.55 value predicted by general relativity assuming a flat LCDM cosmology. In the third work, we present a new parameterization of the linear growth rate for the Horndeski class of modified-gravity theories by generalizing the constant growth index parameterization into a two-parameter redshift-dependent one. The new parameterization is validated assuming stringent constraints from Stage IV and V large-scale structure surveys and is shown to improve the median chi squared of the fit to viable Horndeski models by a factor of ~40 relative to that of a constant growth index.PHDPhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/177978/1/ywwen_1.pd