On the Unlikeliness of Multi-Field Inflation: Bounded Random Potentials and our Vacuum

TL;DR

This paper uses random matrix theory to analyze the likelihood of different critical points in bounded multi-field potentials, concluding that high-dimensional inflation is rare and favors low-dimensional field spaces for our universe.

Contribution

It introduces a model of bounded random potentials with non-zero mean mass matrices and analyzes the probability of inflationary scenarios in high-dimensional field spaces.

Findings

Inflation is rare in high-dimensional field spaces, occurring near saddle points.

Bounded potentials make minima and maxima more common at low potential values.

Low-dimensional field spaces are favored for our universe's inflationary history.

Abstract

Based on random matrix theory, we compute the likelihood of saddles and minima in a class of random potentials that are softly bounded from above and below, as required for the validity of low energy effective theories. Imposing this bound leads to a random mass matrix with non-zero mean of its entries. If the dimensionality of field-space is large, inflation is rare, taking place near a saddle point (if at all), since saddles are more likely than minima or maxima for common values of the potential. Due to the boundedness of the potential, the latter become more ubiquitous for rare low/large values respectively. Based on the observation of a positive cosmological constant, we conclude that the dimensionality of field-space after (and most likely during) inflation has to be low if no anthropic arguments are invoked, since the alternative, encountering a metastable deSitter vacuum by chance, is extremely unlikely.