In the era of precision cosmology, cosmologists use extensive data sets to test theories about the structure and evolution of the universe. The standard cosmological model is consistent with all current data, including many independent measurements based on different physics, but mysteries such as dark energy and dark matter remain. I propose new methods for applying current and future data to probe the following important assumptions underlying standard analyses: the law of gravity at megaparsec scales, the shape of the primordial power spectrum (PPS), and the relationship between the Sunyaev-Zel'dovich (SZ) effect and the mass of galaxy clusters. In the current understanding of the universe, general relativity is extrapolated to length scales twelve orders of magnitude beyond the scales of previous experimental tests. To test this extrapolation, we place the first constraints on deviations from the inverse-square law on megaparsec scales. We examine the growth of large-scale structure (LSS) under a perturbed law of gravity, and compare the resulting deviation in the power spectrum to data from two LSS surveys. No evidence is found for any deviations from normal gravity. The standard cosmological model also assumes a nearly scale-invariant spectrum of initial density fluctuations, often parameterized by a power-law PPS. We apply a smoothing spline, a non-parametric statistical method, to reconstruct the shape of the PPS from cosmic microwave background (CMB) data. Our analysis finds no significant indication that the PPS deviates from a power law. Furthermore, smooth variations in the PPS are not significantly degenerate with other cosmological parameters. Future galaxy redshift surveys will observe thousands of galaxy clusters through the SZ effect. This data could constrain cosmology, including dark energy properties, if we assume a relation between cluster mass and SZ flux. We show how to directly probe this relation by combining measurements of the weak gravitational lensing of distant galaxies by multiple clusters. Such an analysis could be used to understand cluster physics, such as radiational cooling, heating from supernova, and feedback from active galactic nuclei.