2005/12/31 by Amir Aazami, Richard Easther · 87 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Constant (computer programming) #Cosmology #Cosmology and Gravitation Theories #Galaxies: Formation, Evolution, Phenomena #Hessian matrix #Limit (mathematics) #Matrix (chemical analysis) #Maxima and minima #Random matrix #String (physics) #hep-th
paper · pdf · doi:10.1088/1475-7516/2006/03/013
published in Journal of Cosmology and Astroparticle Physics 2006(03), 013 (Institute of Physics) · revtex, 3 figures, 10 pages v2 refs added
arxiv created 2006/01/23 · openalex publication_date 2006/03/15 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
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 analyse the Hessian matrices associated with the extrema of this potential. These potentials generically have a vast number of extrema. We show that if the cross-couplings (off-diagonal terms) are of the same order as the self-couplings (diagonal terms), essentially all extrema are saddles, and the number of minima is effectively zero. Avoiding this requires the same separation of scales as is 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.