A Smooth Landscape: Ending Saddle Point Inflation Requires Features to be Shallow

TL;DR

This paper analyzes saddle point inflation in string theory landscapes, showing that to match observations, features must be shallow, which constrains the landscape's structure and the resulting non-Gaussianities.

Contribution

It demonstrates that shallow features are necessary in the landscape to produce viable inflation and consistent non-Gaussianities, providing a justification for modeling landscapes with smooth, truncated Fourier series.

Findings

Shallow features produce acceptable non-Gaussianities.

Deep features lead to large, potentially inconsistent non-Gaussianities.

Shallow landscape features are essential for realistic inflation models.

Abstract

We consider inflation driven near a saddle point in a higher dimensional field space, which is the most likely type of slow roll inflation on the string theoretical landscape; anthropic arguments need to be invoked in order to find a sufficiently flat region. To give all inflatons large masses after inflation and yield a small but positive cosmological constant, the trajectory in field space needs to terminate in a hole on the inflationary plateau, introducing a curved end-of-inflation hypersurface. We compute non-Gaussianities (bi- and tri-spectrum) caused by this curved hyper-surface and find a negative, potentially large, local non-linearity parameter. To be consistent with current observational bounds, the hole needs to be shallow, i.e. considerably wider than deep in natural units. To avoid singling out our vacuum as special (i.e. more special than a positive cosmological constant entails), we deduce that all features on field space should be similarly shallow, severely limiting the type of landscapes one may use for inflationary model building. We justify the use of a truncated Fourier series with random coefficients, which are suppressed the higher the frequency, to model such a smooth landscape by a random potential, as is often done in the literature without a good a priory reason.