Cosmological Inflation in N-Dimensional Gaussian Random Fields with Algorithmic Data Compression

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 observatio