Minimal Supergravity Models of Inflation

TL;DR

Ferrara, Kallosh, Linde, and Porrati introduce a master superconformal framework in which a single real inflaton from a vector or linear multiplet drives inflation via D-term potentials. The approach yields both Higgs and de-Higgs phases and supports dual formulations, including a linear-multiplet (tensor) description, while avoiding moduli stabilization due to the absence of extra vevs during inflation. It generalizes to simple chaotic potentials, broader polynomial forms, and universal attractor classes (including Starobinsky and T-model) with robust predictions for ns and r, governed by SU(1,1) and related geometric structures. The work provides an economical, symmetry-based bridge between Planck-era cosmology and supergravity, offering flexible yet minimal ingredients to fit observational data and enabling future exploration of reheating and SUSY breaking within this framework.

Abstract

We present a superconformal master action for a class of supergravity models with one arbitrary function defining the Jordan frame. It leads to a gauge-invariant action for a real vector multiplet, which upon gauge fixing describes a massive vector multiplet, or to a dual formulation with a linear multiplet and a massive tensor field. In both cases the models have one real scalar, the inflaton, naturally suited for single-field inflation. Vectors and tensors required by supersymmetry to complement a single real scalar do not acquire vev's during inflation, so there is no need to stabilize the extra scalars which are always present in the theories with chiral matter multiplets. The new class of models can describe any inflaton potential which vanishes at its minimum and grows monotonically away from the minimum. In this class of supergravity models one can fit any desirable choice of inflationary parameters n_s and r.

Figures (5)

• Figure 1: Inflationary potential ${g^{2}{\varphi}^{2}\over 2} (1-a{\varphi}+b{\varphi}^{2})^2$ (\ref{['three']}), for $a = 0.1$, $b = 0.0035$. The field is shown in Planck units, the potential $V$ is shown in units $g^{2}$. In realistic models of that type, $g \sim 10^{-5} - 10^{-6}$ in Planck units, depending on details of the theory, so the height of the potential in this figure is about $10^{-10}$ in Planck units.
• Figure 2: Relation between the canonical variable ${\varphi}$ and the original variable $C$ in the theory (\ref{['three']}).
• Figure 3: Inflationary potential ${g^{2}{\varphi}^{2}\over 2} (1-a{\varphi}+b{\varphi}^{2})^2$ (\ref{['three']}) as a function of the field $C$.
• Figure 4: The function $D(C)$. As we see, $D' <0$, so the condition $D'(C)<0$ is satisfied.
• Figure 5: The potential of the T-Model as a function of the field $C$. The height of the potential is given in units of $V_{*}$.