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 ns∼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.
Highlights
Introduction and SummaryThere have been many discussions of single-field models of chaotic inflation based on renormalizable polynomial potentials [1], i.e., combinations of φn : n ≤ 4
Prior to the Planck data on the Cosmic Microwave Background (CMB) [2], upper limits on the ratio r of tensor and scalar density perturbations and measurements of the scalar index ns from WMAP [3] and other CMB experiments already disfavoured φ4 models quite strongly, and φ2 models were marginal
We show that the model yields enough e-folds of inflation if the value of v is large enough, typically MPl, and that the tensor-to-scalar ratio r can be arbitrarily small in the limit where the initial value of the inflaton field φ0 → 1/2−
Summary
There have been many discussions of single-field models of chaotic inflation based on renormalizable polynomial potentials [1], i.e., combinations of φn : n ≤ 4. We show that the model yields enough e-folds of inflation if the value of v is large enough, typically MPl, and that the tensor-to-scalar ratio r can be arbitrarily small in the limit where the initial value of the inflaton field φ0 → 1/2− This simple single-field model is very consistent with the Planck CMB data [2]. In the case of the Wess-Zumino extension (2) of the minimal model, one may parametrize the complex scalar component of Φ as φeiθ and recover the simplified model (1) in the limit θ → 0, identifying A = λ2 and v = μ/λ In this case, a secondary minimum at φ = 0 appears only for cos θ > 8/9, and is energetically disfavoured for cos θ < 1. We conclude with some remarks about the possible compatibility of the Wess-Zumino model (2) with a supersymmetric seesaw model of neutrino masses, pointing out that this would violate R-parity, though not jeopardizing the possibility that the lightest supersymmetric particle might provide the astrophysical cold dark matter
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