Date of Award
Bachelor of Science
Dr. Ted Bunn
The leading modern theories of cosmological inﬂation are increasingly multi-dimensional. The “inﬂaton ﬁeld” φ that has been postulated to drive accelerating expansion in the very early universe has a corresponding potential function V , the details of which, such as the number of dimensions and shape, have yet to be speciﬁed. We consider a natural hypothesis that V ought to be maximally random. We realize this idea by deﬁning the V as a Gaussian random ﬁeld in some number N of dimensions. We repeatedly simulate of the evolution of φ given a set of conditions on the “landscape” of V . We simulate a “path” stepwise through φ-space while simultaneously computing V and its derivatives along the path via a constrained Gaussian random process, incorporating the information from prior steps. When N is large, this method signiﬁcantly reduces computational load as compared to methods which generate the potential landscape all at once. Even so, computation of the covariance matrix Γ of constraints on V can quickly become intractable. Inspired by this problem, we present data compression algorithms to prioritize the necessary information already simulated, then keep an arbitrarily large portion. Information such as the evolution of the scale factor and tensor and scalar perturbations can be extracted from any particular path, then statistical information about these quantities can be gathered from repeated trials. In these ways, we present a versatile multi-variable program for exploration into how accurately this emergent model can ﬁt to observation
Painter, Connor A., "Cosmological Inﬂation in N-Dimensional Gaussian Random Fields with Algorithmic Data Compression" (2021). Honors Theses. 1556.