Cosmological Attractors and Initial Conditions for Inflation

TL;DR

This paper refines supergravity-based $ ext{α}$-attractor inflation models by constructing stable, shift-symmetric Kahler potentials, demonstrating that natural initial conditions for inflation arise from the model's geometric properties and potential shape.

Contribution

The authors develop a refined class of supergravity $ ext{α}$-attractor models with built-in shift symmetry, ensuring stability and natural initial conditions for inflation without additional stabilization.

Findings

Models are stable with respect to all scalar fields at all $ ext{α}$ values.

The inflaton potential features a nearly Minkowski minimum and an infinite dS valley.

Initial inflaton conditions are naturally set at large values due to the model's geometry.

Abstract

Inflationary $\alpha$-attractor models in supergravity, which provide excellent fits to the latest observational data, are based on the Poincare disk hyperbolic geometry. We refine these models by constructing Kahler potentials with built-in inflaton shift symmetry and by making a canonical choice of the goldstino Kahler potential. The refined models are stable with respect to all scalar fields at all $\alpha$, no additional stabilization terms are required. The scalar potential V has a nearly Minkowski minimum at small values of the inflaton field $\varphi$, and an infinitely long dS valley of constant depth and width at large $\varphi$. Because of the infinite length of this shift-symmetric valley, the initial value of the inflaton field at the Planck density is expected to be extremely large. We show that the inflaton field $\varphi$ does not change much until all fields lose their energy and fall to the bottom of the dS valley at large $\varphi$. This provides natural initial conditions for inflation driven by the inflaton field slowly rolling along the dS valley towards the minimum of the potential at small $\varphi$. A detailed description of this process is given for $\alpha$-attractors in supergravity, but we believe that our general conclusions concerning naturalness of initial conditions for inflation are valid for a broad class of inflationary models with sufficiently flat potentials.