Exploring Two-Field Inflation in the Wess-Zumino Model

Abstract

We explore inflation via the effective potential of the minimal Wess-Zumino model, considering both the real and imaginary components of the complex field. Using transport techniques, we calculate the full allowed range of $n_s$, $r$ and $f_{\rm NL}$ for different choices of the single free parameter, $v$, and present the probability distribution of these signatures given a simple choice for the prior distribution of initial conditions. Our work provides a case study of multi-field inflation in a simple but realistic setting, with important lessons that are likely to apply more generally. For example, we find that there are initial conditions consistent with observations of $n_s$ and $r$ for values of $v$ that would be excluded if only evolutions in the real field direction were to be considered, and that these may yield enhanced values of $f_{\rm NL}$. Moreover, we find that initial conditions fixed at high energy density, where the potential is close to quartic in form, can still lead to evolutions in a concave region of the potential during the observable number of e-folds, as preferred by present data. The Wess-Zumino model therefore provides an illustration that multi-field dynamics must be taken into account when seeking to understand fully the phenomenology of such models of inflation.