Cosmological Inflation in N-Dimensional Gaussian Random Fields with
  Algorithmic Data Compression
  There is considerable interest in inflationary models with multiple inflaton
fields. The inflaton field $\boldsymbol\phi$ has a corresponding potential
function $V$, the details of which, such as the number of dimensions and shape,
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 set of
parameters that statistically determine the shape of $V$, we repeatedly evolve
$\boldsymbol\phi$ through the end of inflation from various initial conditions,
cataloguing a representative sample of trajectories associated with that model.
In order to impose the anthropic constraint of a universe in which inflation
ends and normal expansion takes over, 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 constrained Gaussian random process. When
$N$ is large, this method significantly reduces computational load as compared
to methods which generate the potential landscape all at once. Even so, the
covariance matrix $\boldsymbol\Gamma$ 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 with various parameter sets, extract tensor and scalar
perturbation spectra from each, 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.
