Abstract
We prove that all inflationary models, including those with dark energy after the end of inflation, can be embedded in minimal supergravity with a single chiral superfield. Moreover, the amount of supersymmetry breaking is independently tunable due to a degeneracy in the choice for the superpotential. The inflaton is a scalar partner of the Goldstino in this set-up. We illustrate our general procedure with two examples that are favoured by the Planck data.
Highlights
We prove that all inflationary models, including those with dark energy after the end of inflation, can be embedded in minimal supergravity with a single chiral superfield
The same issue was addressed in [13, 14] depending on the angle between the two directions of inflation and the sGoldstini
In this letter we will prove a comparable versatility for sGoldstino inflation: all inflationary potentials can be realized in a single-superfield construction
Summary
The scalar dynamics of general supergravity models is specified in terms of two quantities. With the Kahler metric KΦΦ ≡ KΦ−Φ1 and the Kahler covariant derivative DΦW ≡ ∂ΦW + KΦW The latter are covariant under the Kahler transformations W → ef W and K → K −f −fwith holomorphic f (Φ), which leave the scalar potential invariant. This implies that the Kahler invariant function satisfies G(Φ, Φ ) = G(Φ , Φ) These properties guarantee that the truncation to Φ = Φ , specifying the trajectory along which inflation will take place, will be a consistent one: the field equation for the imaginary component of Φ is satisfied along the trajectory Φ = Φfor arbitrary choices of Kahler and superpotentials satisfying the above criteria.. The Kahler potential vanishes, K = 0, along the inflationary trajectory This consistutes a shift symmetry of the inflaton field and implies that KΦ = 0 along Φ = Φ. Describing a flat and hyperbolic manifold in terms of coordinates Φ and T , respectively
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