Wess-Zumino Inflation in Light of Planck
Djuna Croon, John Ellis, Nick E. Mavromatos
TL;DR
The paper analyzes inflation in the minimal Wess-Zumino model with a single massive chiral supermultiplet and shows that a renormalizable single-field potential can yield $n_s \sim 0.96$ and $r < 0.1$, in agreement with Planck, under suitable parameters and initial conditions. Using the effective potential $V = A v^4 ( x^4 - 2 \cos \theta x^3 + x^2)$ with $x=\phi/v$, the authors derive slow-roll observables and demonstrate compatibility across a range of $x_i$ and $N$ values, with $v^2/M_{Pl}^2 \gg 1$. The work extends to the full Wess-Zumino model including an angular degree of freedom and discusses possible topological inflation and a seesaw-based neutrino mass sector with small $R$-parity violation. The results provide a simple, Planck-compatible inflationary scenario with potential implications for domain-wall inflation, future $r$-bounds, and supersymmetric neutrino physics.
Abstract
We discuss cosmological inflation in the minimal Wess-Zumino model with a single massive chiral supermultiplet. With suitable parameters and assuming a plausible initial condition at the start of the inflationary epoch, the model can yield scalar perturbations in the Cosmic Microwave Background (CMB) of the correct strength with a spectral index n_s ~ 0.96 and a tensor-to-scalar perturbation ratio r < 0.1, consistent with the Planck CMB data. We also discuss the possibility of topological inflation within the Wess-Zumino model, and the possibility of combining it with a seesaw model for neutrino masses. This would violate R-parity, but at such a low rate that the lightest supersymmetric particle would have a lifetime long enough to constitute the astrophysical cold dark matter.