Singularities in Semiclassical Cosmology

The semi-classical Einstein equation (SEE) is an attempt to rectify the classical nature of Einstein’s field equations in our quantum universe: the matter portion of Einstein’s equation, the energy-momentum tensor, is quantized. This project analyzes which conditions today lead to a primordial singularity in the past within our universe in the context of the SEE. We use derived solutions of the SEE for a scalar field in an FLRW universe for our analysis. In this context, we define a singularity occurrence to be when the scale factor within the FLRW metric goes to zero. The investigation of the existence of singularities was performed by varying the initial conditions of a variety of parameters, checking simpler, bounding differential equations, and using analytical and numerical methods.