Abstract
We study higher order corrections in new minimal supergravity models of a single scalar field inflation. The gauging in these models leads to a massive vector multiplet and the D-term potential for the inflaton field with a coupling g2 ∼ 10−10. In the de-Higgsed phase with vanishing g2, the chiral and vector multiplets are non-interacting, and the potential vanishes. We present generic manifestly supersymmetric higher order corrections for these models. In particular, for a supersymmetric gravity model −R+R2 we derive manifestly supersymmetric corrections corresponding to Rn. The dual version corresponds to a standard supergravity model with a single scalar and a massive vector. It includes, in addition, higher Maxwell curvature/scalar interaction terms of the Born-Infeld type and a modified D-term scalar field potential. We use the dual version of the model to argue that higher order corrections do not affect the last 60 e-foldings of inflation; for example the ξR4 correction is irrelevant as long as ξ < 1024.
Highlights
There are several different ways to protect flatness of the inflationary potential
As we will see, this problem does not appear in the context of the new approach to supergravity inflation proposed in [1]: If we take the first term in the expansion of the potential proportional to g2, which takes the role of the parameter m2 in the example described above, all terms higher order in the inflaton field will be automatically suppressed by the small constant g2, or by even smaller factors g2n
We will focus on the study of new minimal supergravity models of inflation [1], [2] of a single scalar field inflation defined by a choice of the Jordan frame function
Summary
A generic superconformal action containing higher powers of the superfield W can be given in the following form: ak,l,p gn. The higher powers of the Maxwell superfield, W N , are dual to a supersymmetric version of RN and will be constructed here In this case the generic functions ΨN (C) will be identified from the requirement of duality to pure gravitational multiplet. The corresponding supersymmetric version of the −R + αR2 gravity was constructed in [7] and the dual model is a standard supergravity, where the R2 term is traded for two chiral multiplets. √ Here we may switch to the canonically normalized scalar φ, where C = −e 2/3φ This corresponds to the scalar-dependent model which is dual to the one defined by the generic pure gravity action f. In gauged supergravity with g = 0, the auxiliary field Ddefines the D-term potential We see this phenomenon already at the non-supersymmetric level. We are ready to evaluate our higher order corrections and find whether they may affect inflation
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