Starobinsky-like Inflationary Models as Avatars of No-Scale Supergravity

TL;DR

The paper demonstrates that Starobinsky-like inflation naturally arises within no-scale supergravity, specifically in the $SU(2,1)/SU(2)\times U(1)$ coset with two complex fields. By selecting appropriate superpotentials, the inflaton can be a modulus or a matter field, and viable stabilization schemes exist that preserve the Starobinsky potential. The authors provide explicit examples showing how the Starobinsky potential is recovered and explore generalizations that modify the predicted tensor-to-scalar ratio $r$ while preserving the spectral tilt $n_s$. They discuss how current Planck constraints and future CMB measurements can probe these embeddings, potentially linking inflationary observables to features of string compactifications and no-scale K"ahler geometry.

Abstract

Models of cosmological inflation resembling the Starobinsky R + R^2 model emerge naturally among the effective potentials derived from no-scale SU(N,1)/SU(N) x U(1) supergravity when N > 1. We display several examples in the SU(2,1)/SU(2) x U(1) case, in which the inflaton may be identified with either a modulus field or a matter field. We discuss how the modulus field may be stabilized in models in which a matter field plays the role of the inflaton. We also discuss models that generalize the Starobinsky model but display different relations between the tilt in the spectrum of scalar density perturbations, n_s, the tensor-to-scalar ratio, r, and the number of e-folds, N_*. Finally, we discuss how such models can be probed by present and future CMB experiments.

Figures (2)

• Figure 1: The potential $V(x)$ evaluated at $\langle t (x) \rangle$ for several choices of $\Lambda^2$ in Planck units, as indicated. For $\Lambda^2 \hbox{$\;\stackrel{<}{\sim}\;$} 0.02$, the potential is indistinguishable from the potential in (\ref{['r2pot']}). In the left panel, a constant was added to the superpotential, while in the right panel, an explicit mass term was added.
• Figure 2: The scalar potential in the $(Re~T, Re~\phi)$ space using the coordinates defined in connection with (\ref{['xt']}), for $Im~T = Im~\phi = 0$.