On the problem of initial conditions for inflation

TL;DR

The paper addresses whether inflation with plateau potentials requires finely tuned initial conditions and argues that it does not for a broad class of models. It shows that inflation can start at Planck densities and then settle onto a plateau described by $V_{0}$, with predictions governed primarily by $\alpha$ and $V_{0}$ in $\alpha$-attractor frameworks, leading to robust, universal observables across varied potentials. It also introduces a simple short-plateau chaotic inflation as a concrete route and extends to two-field and singular-boundary α-attractors, demonstrating asymptotic decoupling of fields and stability against quantum corrections. These results bolster the viability of Planck-favored inflationary scenarios (e.g., GL, Starobinsky, Higgs inflation, and $\alpha$-attractors) and mitigate concerns about initial-condition fine-tuning, including inhomogeneous and topologically nontrivial settings.

Abstract

I review the present status of the problem of initial conditions for inflation and describe several ways to solve this problem for many popular inflationary models, including the recent generation of the models with plateau potentials favored by cosmological observations.

Figures (1)

• Figure 1: The potential $V(\phi) = {m^{2}\phi^{2}\over 2}\,\bigl(1-a\phi +a^{2}b\,\phi^{2}\bigr)$ for $a = 0.12$ and $b = 0.30$ (upper curve), $b = 0.29$ (middle), and $b = 0.28$ (lower curve). The potential is shown in units of $m^{2}$, with $\phi$ in Planck units. For $b = 0.29$ (the middle curve), at the moment corresponding to $N= 58$ e-folding from the end of inflation one has $n_{s}= 0.965$ and $r = 0.012$, perfectly matching the Planck data.