Revisiting Witten-O'Raifeartaigh Inflation for a Non-minimally Coupled Scalar Field

Abstract

In this work, we revisit the Witten-O'Raifeartaigh model of inflation, in which the potential takes a $\operatorname{log}^2(\phi/M)$ form, when the scalar field is non-minimally coupled to gravity. We investigate the impact of the coupling in the prediction of the inflationary parameters, thereby affecting the viability of the model. We find that a small coupling of order $\xi\sim10^{-3}$ is preferred by data at the $n_s-r$ plane level, and that the presence of a non-zero $\xi$ allows for a large interval of the mass scale $M$, in which it is possible to achieve a low tensor-to-scalar ratio. We also establish constraints imposed by a subsequent reheating era, in which its duration and temperature can be related to CMB observables, which in return, restricts the possible values for the $n_s$ and $r$ parameters.