Large-Field Inflation and Supersymmetry Breaking

TL;DR

This paper investigates how large-field chaotic inflation can be embedded in supergravity when coupled to supersymmetry breaking sectors. It analyzes minimal (Polonyi) and extended (with an X–φ coupling) setups, as well as an O'Raifeartaigh model, and also considers chaotic inflation without a stabilizer field but with a stabilized modulus. A key finding is that in all viable models the gravitino mass is bounded above by the inflationary scale, typically $m_{3/2} \lesssim m$ and often $m_{3/2} \lesssim H$, implying tension with high-scale SUSY breaking, especially under moduli stabilization. The work concludes that gravity-mediated couplings are necessary for consistency and that no-stabilizer constructions with stabilized moduli do not cure the potential's instability; these results constrain high-scale SUSY scenarios in chaotic inflation contexts.

Abstract

Large-field inflation is an interesting and predictive scenario. Its non-trivial embedding in supergravity was intensively studied in the recent literature, whereas its interplay with supersymmetry breaking has been less thoroughly investigated. We consider the minimal viable model of chaotic inflation in supergravity containing a stabilizer field, and add a Polonyi field. Furthermore, we study two possible extensions of the minimal setup. We show that there are various constraints: first of all, it is very hard to couple an O'Raifeartaigh sector with the inflaton sector, the simplest viable option being to couple them only through gravity. Second, even in the simplest model the gravitino mass is bounded from above parametrically by the inflaton mass. Therefore, high-scale supersymmetry breaking is hard to implement in a chaotic inflation setup. As a separate comment we analyze the simplest chaotic inflation construction without a stabilizer field, together with a supersymmetrically stabilized Kahler modulus. Without a modulus, the potential of such a model is unbounded from below. We show that a heavy modulus cannot solve this problem.

Figures (3)

• Figure 1: Evolution of the canonically normalized imaginary part of $S$ (a) and the inflaton $\varphi$ (b) during inflation, for $\xi_1 = \xi_2 = 10$ and $f = 10^{-8}$. In this case, since $f < m$, cancellation of the cosmological constant implies $W_0^2 = \frac{f^2}{3}$. Depending on its initial value the stabilizer field settles in its shifted minimum very early and remains stabilized for the rest of the inflationary epoch and beyond (notice the different time scales in the plots). Due to its inflaton-dependence, the vev of $S$ evolves with time.
• Figure 2: $n_s$ and $r$ as a function of the supersymmetry breaking scale $f$. Clearly, the model is ruled out by observation at values of $f$ quite below $10^{-4}$.
• Figure 3: CMB observables as functions of the supersymmetry breaking scale $f$, for different values of $\delta$ and $m=6\times 10^{-6}$, $\xi_1=10$ in Planck units.