Inflation in random Gaussian landscapes

Abstract

We develop analytic and numerical techniques for studying the statistics of slow-roll inflation in random Gaussian landscapes. As an illustration of these techniques, we analyze small-field inflation in a one-dimensional landscape. We calculate the probability distributions for the maximal number of e-folds and for the spectral index of density fluctuations $n_s$ and its running ${\alpha }_s$. These distributions have a universal form, insensitive to the correlation function of the Gaussian ensemble. We outline possible extensions of our methods to a large number of fields and to models of large-field inflation. These methods do not suffer from potential inconsistencies inherent in the Brownian motion technique, which has been used in most of the earlier treatments.

25 pages, 6 figures

References in corpus (6)

• Efficient numerical solution to vacuum decay with many fields
• Cosmology From Random Multifield Potentials
• Accidental Inflation in String Theory
• Exploring a string-like landscape
• On the Unlikeliness of Multi-Field Inflation: Bounded Random Potentials and our Vacuum
• Random Functions via Dyson Brownian Motion: Progress and Problems

Cited by in corpus (22)

• Primordial Black Holes from Polynomial Potentials in Single Field Inflation
• Conditions for (No) Eternal Inflation
• CMB targets after the latest Planck data release
• Adiabatic suppression of the axion abundance and isocurvature due to coupling to hidden monopoles
• Manyfield Inflation in Random Potentials
• Classical transitions with the topological number changing in the early Universe
• Seven Lessons from Manyfield Inflation in Random Potentials
• Inflation in Multi-field Modified DBM Potentials
• Hessian eigenvalue distribution in a random Gaussian landscape
• Initial conditions for slow-roll inflation in a random Gaussian landscape
• Inflation in multi-field random Gaussian landscapes
• Towards a complete mass spectrum of type-IIB flux vacua at large complex structure
• Learning to Inflate
• Anthropic Bound on Dark Radiation and its Implications for Reheating
• Transitions between topologically non-trivial configurations
• Inflation in Random Landscapes with two energy scales
• Cosmic Perturbations from a Rotating Field
• Note on initial conditions for small-field inflation
• 4-volume cutoff measure of the multiverse
• The Distribution of Vacua in Random Landscape Potentials
• Slepian models for Gaussian Random Landscapes
• New Inflation in the Landscape and Typicality of the Observed Cosmic Perturbation