Testing Gravity with Cosmology: Unlocking the secrets of cosmic acceleration
In the era of precision cosmology, large cosmological surveys are mapping the Cosmic Microwave Background like the Planck Space Observatory, the Atacama Cosmology Telescope (ACT), and the future Simons Observatory (SO). Furthermore, surveys are mapping vast sets of galaxies like the Sloan Digital Sky Survey (SDSS), the Dark Energy Spectroscopic Instrument (DESI), and the upcoming Roman Space Telescope. In this thesis, we carefully analyze currently available datasets to put new constraints on gravity and develop crucial foundations to prepare for upcoming datasets that offer new opportunities to probe the growth of structure in the universe. These allow us to build differentiating tests of gravity, ultimately leading to an understanding of the nature of dark energy. To make optimal use of upcoming datasets, we simultaneously need to advance our analysis techniques and build precision tests. This includes carefully considering how we can optimize cosmological constraining power by choosing the survey designs and how to combine different datasets. We also need a precise understanding of the systematic effects involved in the measurement to give confidence in the resulting cosmological constraints. And finally, we need precision estimators for our cosmological tests that are appropriate for upcoming datasets.