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There is considerable interest in inflationary models with multiple inflatonfields. The inflaton field $\boldsymbol\phi$ that has been postulated to driveaccelerating expansion in the very early universe has a corresponding potential$V$, the details of which are free parameters of the theory. We consider anatural hypothesis that $V$ ought to be maximally random. We realize this ideaby defining $V$ as a Gaussian random field in some number $N$ of dimensions.Given a model that statistically determines the shape of $V$, we repeatedlyevolve $\boldsymbol\phi$ under random potentials, cataloging a representativesample of trajectories associated with that model. On anthropic grounds, weimpose a minimum with $V=0$ and only consider trajectories that reach thatminimum. We simulate each path evolution stepwise through$\boldsymbol\phi$-space while simultaneously computing $V$ and its derivativesalong the path via a Gaussian random process. When $N$ is large, this methodsignificantly reduces computational load as compared to methods that generatethe potential landscape all at once. Even so, the covariance matrix ofconstraints on $V$ can quickly become large and cumbersome. To solve thisproblem, we present data compression algorithms to prioritize the necessaryinformation already simulated, then keep an arbitrarily large portion. Withthese optimizations, we simulate thousands of trajectories, extract matter,tensor, and isocurvature spectra from each, and then assemble statisticalpredictions of these quantities through repeated trials. We find that theGaussian random potential is a highly versatile inflationary model with a richvolume of parameter space capable of reproducing modern observations.

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