**Student**: Kenneth Heitritter, PhD student in Physics, University of Iowa

**Faculty Advisor: Vincent G. J. Rodgers**

**Cosmological and Quantum Gravitational Implications of Projective Connections**

Einstein’s theory of gravity, known as general relativity, is one of the most robustly tested physical theories of the modern-day. Even so, it is not without its shortcomings. Namely, general relativity is known as a classical theory of physics and therefore does not take into account the fundamentally quantum nature of all physics. Much effort has been put into the development of a quantum theory of gravity in the forms of string theory and loop quantum gravity. My research is concerned with understanding the implications of a somewhat overlooked physical field, which was first noticed in two-dimensional quantum gravity. This field is known as the diffeomorphism field and has recently been shown to arise as a component in a so-called projective connection. By building a dynamical theory of these projective connections, one finds both Einstein’s theory of general relativity as well as additional contributions from the diffeomorphism field. Under certain assumptions, I show that this additional field can give rise to a model that fits all experimental data regarding cosmological inflation, a period in the early the universe when rapid expansion occurred. This discovery could shed light on issues of quantum gravity which known methods have missed.