Natural $\alpha$-Attractors from ${\cal N}=1$ Supergravity via flat K\"ahler Manifolds

TL;DR

This paper develops a new class of $ ext{α}$-attractor inflation models within ${ m N}=1$ supergravity using flat K"ahler manifolds, featuring a shift symmetry and a potential with a long de Sitter valley leading to a Minkowski minimum.

Contribution

It introduces $ ext{α}$-attractor models based on flat K"ahler manifolds with a specific logarithmic K"ahler potential form and shift symmetry, expanding the framework of supergravity inflation models.

Findings

Scalar potential has an infinitely long de Sitter valley at large inflaton values.

Potential attains a Minkowski minimum at small inflaton values.

Models demonstrate the viability of flat K"ahler manifolds in supergravity inflation.

Abstract

We present $\alpha$-attractor models for inflation based on ${\cal N}=1$ supergravity with flat K\"ahler manifolds. The function form of the associated K\"ahler potential in these models are logarithmic square in nature and has a visible shift symmetry in its composite canonical variables. The scalar potential $V$ with respect to these field variables has an infinitely long dS valley of constant depth and width at large values of inflaton field $\psi$ and attains a Minkowski minimum at small $\psi$. We illustrate this new framework with a couple of examples.