Building and testing models of cosmic inflation with modified gravity

Cosmic inflation, the idea that the very early universe underwent a dramatic accelerating expansion of space, has found great success in explaining aspects of the universe that were previously poorly understood. As a result, it has gained popularity and traction in the scientific mainstream in recent decades. However, it is still unclear exactly how inflation could have occurred; nothing in the established laws of physics can explain it. Now, in the modern era of precision cosmology, experimental data capable of probing and testing the details of this epoch has become available. With this, a deeper understanding of the physics of inflation may be possible, and it may prove to be the key to unlocking some of the greatest unsolved mysteries in theoretical physics. In this thesis, models of beyond-standard-model physics, with a particular focus on those inspired by modified theories of gravity (those that extend Einstein's theory of General Relativity), are studied with the goal of understanding their inflationary consequences and hence establish how feasible these exotic theories are as descriptions of the early universe from this perspective. Additionally, some thought is given to present and future tests of inflation as well as how new data, or improvements in the presently available data, will increase cosmologists' ability to discriminate between different theories of inflation and hence move closer to answering the question of what caused it once and for all.