Cosmology From Random Multifield Potentials

TL;DR

This paper studies the statistical properties of vacua and inflationary paths in random multifield potentials, revealing that most extrema are saddles and that the landscape's structure poses challenges for inflation models.

Contribution

It applies random matrix theory to analyze the Hessian matrices of multifield potentials, providing new insights into the nature of extrema and their implications for cosmology.

Findings

Most extrema are saddles when off-diagonal couplings are comparable to diagonal ones.

The typical distance between extrema remains large despite a vast number of extrema.

Implications for inflationary models include difficulties in navigating the landscape.

Abstract

We consider the statistical properties of vacua and inflationary trajectories associated with a random multifield potential. Our underlying motivation is the string landscape, but our calculations apply to general potentials. Using random matrix theory, we analyze the Hessian matrices associated with the extrema of this potential. These potentials generically have a vast number of extrema. If the cross-couplings (off-diagonal terms) are of the same order as the self-couplings (diagonal terms) we show that essentially all extrema are saddles, and the number of minima is effectively zero. Avoiding this requires the same separation of scales needed to ensure that Newton's constant is stable against radiative corrections in a string landscape. Using the central limit theorem we find that even if the number of extrema is enormous, the typical distance between extrema is still substantial -- with challenging implications for inflationary models that depend on the existence of a complicated path inside the landscape.