Abstract
We systematically study the renormalizable three-term polynomial inflation in the supersymmetric and non-supersymmetric models. The supersymmetric inflaton potentials can be realized in supergravity theory, and only have two independent parameters. We show that the general renormalizable supergravity model is equivalent to one kind of our supersymmetric models. We find that the spectral index and tensor-to-scalar ratio can be consistent with the Planck and BICEP2 results, but the running of spectral index is always out of the $2\sigma$ range. If we do not consider the BICEP2 experiment, these inflationary models can be highly consistent with the Planck observations and saturate its upper bound on the tensor-to-scalar ratio ($r \le 0.11$). Thus, our models can be tested at the future Planck and QUBIC experiments.
Highlights
The Planck satellite measured the cosmic microwave background radiation (CMB) temperature anisotropy with an unprecedented accuracy
With r = 0.16 or 0.20, we find that the Hubble scale during inflation is about 1.0×1014 GeV, and the inflaton potential is around the Grand Unified Theory (GUT) scale 2×1016 GeV which might have some connections with GUTs
We have systematically studied the renormalizable threeterm polynomial inflation in the supersymmetric and nonsupersymmetric models
Summary
The Planck satellite measured the CMB temperature anisotropy with an unprecedented accuracy. Because these results were announced seven months after we submitted our paper to arXiv, we will not consider them here Such a large tensor-to-scalar ratio r from the BICEP2 measurement does impose a strong constraint on the inflationary models. The supersymmetric inflaton potentials can be obtained from supergravity theory We find that their spectral indices and tensor-to-scalar ratios can be consistent with the Planck and BICEP2 experiments. The tensor-to-scalar ratio cannot only be larger than 0.01 in the 1σ region, above the well-known Lyth bound [16], but it saturates the Planck upper bound 0.11 in the 1σ region These models produce the typical large field inflation, and they can be tested at the future Planck and QUBIC experiments.
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