Does the first chaotic inflation model in supergravity provide the best fit to the Planck data?

TL;DR

This work revisits the first chaotic inflation model in supergravity (the GL model) and clarifies its single-field, plateau-like potential that yields $n_s = 1 - \frac{2}{N}$ and $r = \frac{4}{3 N^{2}}$, consistent with Planck data when $N \sim 50$–60 and $m \sim 7 \times 10^{-6}$. It links the GL construction to the broader α-attractor framework and shows that generalized GL models share the same attractor predictions in the large-$N$ limit, despite diverse small-field behavior. The author extends the model by incorporating a nilpotent field to achieve uplifting to a small positive cosmological constant and to realize SUSY breaking, with $V(0) = c^{2} - 3 d^{2}$ and $m_{3/2} = d$, while demonstrating that the large-$\phi$ predictions remain intact provided $c$ is kept tiny. Overall, the original GL model remains a simple, robust realization of chaotic inflation in supergravity that naturally aligns with current cosmological data and can accommodate late-time acceleration and SUSY breaking through controlled modifications.

Abstract

I describe the first model of chaotic inflation in supergravity, which was proposed by Goncharov and the present author in 1983. The inflaton potential of this model has a plateau-type behavior $V_{0} (1- {8\over 3}\, e^{-\sqrt 6 |φ|})$ at large values of the inflaton field. This model predicts $n_{s} = 1-{2\over N} \approx 0.967$ and $r = {4\over 3 N^{2}} \approx 4 \times 10^{-4}$, in good agreement with the Planck data. I propose a slight generalization of this model, which allows to describe not only inflation but also dark energy and supersymmetry breaking.

Figures (3)

• Figure 1: The thick blue line shows the inflaton potential (\ref{['pot']}) in the theory (\ref{['shift']}), (2.2) in units $m = 1$. The red dashed line shows its asymptotic representation (\ref{['app']}), which exponentially rapidly converges to in the inflationary regime with $\phi \gtrsim 1$. The last 60 e-foldings of the evolution of the universe correspond to $\phi \lesssim 2.8$.
• Figure 2: The scalar potential in the generalized GL model (\ref{['sn']}). The potentials for $n = 1$, 2, 3, 4 are shown by blue, yellow, green and red lines correspondingly.
• Figure 3: The scalar potential in the model (\ref{['attr2']}). After inflation, the field rolls down to one of the two stable supersymmetric Minkowski vacua with $\phi \approx \pm 0.865$ and stays there.