Investigations into alternative theories of cosmology

General relativity and the cosmological concordance model (?CDM) successfully explain a myriad of observations. The perihelion precession of Mercury; the polarization of the cosmic microwave background; the observed baryon acoustic oscillations feature in the matter power spectrum; and the statistics of weak gravitational lensing all contribute to the vindication of the theories. However, these theories fall short in some areas. One of these shortfalls is the explanation of the magnitude of the cosmological constant; another is the tension between late-time and early-time measures of the Hubble constant. The purpose of this thesis is to investigate alternative theories of gravity and cosmology and the possible rectification of their shortcomings. Kaloper & Padilla’s sequester theory decouples the cosmological constant from vacuum loops containing Standard Model particles. The sequestering mechanism is the result of an additional global term, representing a kind of matter which does not gravitate, as other contributions to the action do. This results in a very small effective cosmological constant which is proportional to the historic average of locally excited matter. We gauge the success of the theory by calculating the form of the divergence coming from two-loop Standard Model scalar vacuum diagrams, determining the level of detuning the theory suffers. We also investigate the consequences of adding an additional component to the universe, cubic Galileons, and coupling them disformally to Standard Model matter. This is not an attempt to solve the cosmological constant problem, the cosmological constant remains in the action and the cubic Galileon exists as a sub-dominant contribution to the total energy density. We calculate the analogue of Maxwell’s equations and use the Wentzel-Kramerss-Brillouin (WKB) approximation to find the wave equation for light and in turn, the small discrepancy in the speeds of light and gravity in this theory. Additionally, we also calculate constraints coming from observations of the integrated Sachs Wolfe (ISW) effect, and the phase velocity of light. These are compiled along with already established constraints coming from collider experiments.