Initial conditions for inflation

Abstract

We propose a single-field mechanism that dynamically prepares the initial conditions required for exponential plateau inflation. The inflaton is decomposed into a coarse-grained mode and a high-occupancy, approximately Gaussian band of relativistic nonzero modes. Gaussian--Hartree averaging of the potential produces an exact variance-dependent minimum, which places the coarse-grained field high on the plateau when the excitation variance is large. Under a translation-invariant microcanonical measure, the available phase-space volume is exponentially concentrated near this minimum, while an order-one homogeneous kinetic-energy fraction is exponentially atypical. During expansion, the preparation modes redshift as radiation, $σ^2\propto a^{-2}$ and $ρ_χ\propto a^{-4}$. Although the induced minimum rapidly moves toward the vacuum, the force acting on the coarse-grained mode is bounded by an exponentially small factor, yielding analytic upper limits on its velocity, displacement, and kinetic fraction. We derive a sufficient condition for the subsequent number of slow-roll e-folds and exhibit a benchmark with more than 60 e-folds. The mechanism also motivates correlated finite-onset signatures: large-scale power suppression with decaying oscillations and a variance-convolution bispectrum.