# Initial conditions for slow-roll inflation in a random Gaussian landscape

## TL;DR

This paper models the initial conditions for slow-roll inflation within a random Gaussian landscape, analyzing tunneling probabilities and inflation duration, and finds consistency with observations but low chances for detecting spatial curvature.

## Contribution

It introduces a model of the landscape as a one-dimensional Gaussian potential to compute initial conditions and inflation probabilities, providing new insights into inflationary scenarios.

## Key findings

- Landscape model aligns with observational data
- Probability of detecting spatial curvature is approximately 0.1%
- Tunneling and inflation duration distributions are characterized

## Abstract

In the landscape perspective, our Universe begins with a quantum tunneling from an eternally-inflating parent vacuum, followed by a period of slow-roll inflation. We investigate the tunneling process and calculate the probability distribution for the initial conditions and for the number of e-folds of slow-roll inflation, modeling the landscape by a small-field one-dimensional random Gaussian potential. We find that such a landscape is fully consistent with observations, but the probability for future detection of spatial curvature is rather low, $P \sim 10^{-3}$.