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

Abstract

There is considerable interest in inflationary models with multiple inflaton fields. The inflaton field $\boldsymbol\phi$ that has been postulated to drive accelerating expansion in the very early universe has a corresponding potential $V$, the details of which are free parameters of the theory. We consider a natural hypothesis that $V$ ought to be maximally random. We realize this idea by defining $V$ as a Gaussian random field in some number $N$ of dimensions. Given a model that statistically determines the shape of $V$, we repeatedly evolve $\boldsymbol\phi$ under random potentials, cataloging a representative sample of trajectories associated with that model. On anthropic grounds, we impose a minimum with $V=0$ and only consider trajectories that reach that minimum. We simulate each path evolution stepwise through $\boldsymbol\phi$-space while simultaneously computing $V$ and its derivatives along the path via a Gaussian random process. When $N$ is large, this method significantly reduces computational load as compared to methods that generate the potential landscape all at once. Even so, the covariance matrix of constraints on $V$ can quickly become large and cumbersome. To solve this problem, we present data compression algorithms to prioritize the necessary information already simulated, then keep an arbitrarily large portion. With these optimizations, we simulate thousands of trajectories, extract matter, tensor, and isocurvature spectra from each, and then assemble statistical predictions of these quantities through repeated trials. We find that the Gaussian random potential is a highly versatile inflationary model with a rich volume of parameter space capable of reproducing modern observations.