Inflationary trajectories in cosmological landscapes are likely to be associated with saddle points. Moreover, the downhill directions of a “useful” inflationary saddle must be sufficiently flat to ensure that inflation lasts long enough and in models with more than one downhill direction each of them must satisfy this constraint. This combination of requirements allows us to deduct that almost all inflationary trajectories in a simple random landscape will have a single downhill direction.
Abstract
Random, multifield functions can set generic expectations for landscape-style cosmologies. We consider the inflationary implications of a landscape defined by a Gaussian random function, which is perhaps the simplest such scenario. Many key properties of this landscape, including the distribution of saddles as a function of height in the potential, depend only on its dimensionality, N, and a single parameter, γ, which is set by the power spectrum of the random function. We show that for saddles with a single downhill direction the negative mass term grows smaller, relative to the average mass, as N increases, a result with potential implications for the η-problem in landscape scenarios. For some power spectra Planck-scale saddles have η∼1 and eternal, topological inflation would be common in these scenarios. Lower-lying saddles typically have large η, but the fraction of these saddles which would support inflation is computable, allowing us to identify which scenarios can deliver a universe that resembles ours. Finally, by drawing inferences about the relative viability of different multiverse proposals we also illustrate ways in which quantitative analyses of multiverse scenarios are feasible.
- Low, Easther and Hotchkiss
- Statistical properties of inflationary saddles in Gaussian random landscapes
- JCAP 12 (2022) 014 or ArXiV:2107.09870
We compute the distribution of eigenvalues of the Hessian metrix of second derivatives of the potential as a function of height in the landscape and landscape parameters. The plot here shows the distribution for saddles with a single downhill direction for a specific set of parameters.