No-scale \(\mu \) -term hybrid inflation

The European Physical Journal C, Mar 2017

To solve the fine-tuning problem in \(\mu \)-term hybrid inflation, we will realize the supersymmetry scenario with the TeV-scale supersymmetric particles and intermediate-scale gravitino from anomaly mediation, which can be consistent with the WMAP and Planck experiments. Moreover, we for the first time propose the \(\mu \)-term hybrid inflation in no-scale supergravity. With four scenarios for the \(SU(3)_C\times SU(2)_L\times SU(2)_R\times U(1)_{B-L}\) model, we show that the correct scalar spectral index \(n_s\) can be obtained, while the tensor-to-scalar ratio r is predicted to be tiny, about \(10^{-10}\)–\(10^{-8}\). Also, the \(SU(2)_R\times U(1)_{B-L}\) symmetry breaking scale is around \(10^{14}\) GeV, and all the supersymmetric particles except gravitino are around the TeV scale, while the gravitino mass is around \(10^{9}\)–\(10^{10}\) GeV. Considering the complete potential terms linear in S, we for the first time show that the tadpole term, which is the key for such kind of inflationary models to be consistent with the observed scalar spectral index, vanishes after inflation. Thus, to obtain the \(\mu \) term, we need to generate the supersymmetry breaking soft term \(A^{S \Phi \Phi '}_{\kappa } \kappa S \Phi \Phi '\) due to \(A^{S \Phi \Phi '}_{\kappa }=0 \) in no-scale supergravity, where \(\Phi \) and \(\Phi '\) are vector-like Higgs fields at high energy. We show that the proper \(A^{S \Phi \Phi '}_{\kappa } \kappa S \Phi \Phi '\) term can be obtained in the M-theory inspired no-scale supergravity. We also point out that \(A^{S \Phi \Phi '}_{\kappa }\) around 700 GeV can be generated via the renormalization group equation running from string scale. We briefly comment on the supersymmetry phenomenological consequences as well.

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No-scale \(\mu \) -term hybrid inflation

Eur. Phys. J. C No-scale µ-term hybrid inflation Lina Wu Shan Hu Tianjun Li To solve the fine-tuning problem in μ-term hybrid inflation, we will realize the supersymmetry scenario with the TeV-scale supersymmetric particles and intermediate-scale gravitino from anomaly mediation, which can be consistent with the WMAP and Planck experiments. Moreover, we for the first time propose the μ-term hybrid inflation in no-scale supergravity. With four scenarios for the SU (3)C × SU (2)L × SU (2)R × U (1)B−L model, we show that the correct scalar spectral index ns can be obtained, while the tensor-to-scalar ratio r is predicted to be tiny, about 10−10-10−8. Also, the SU (2)R ×U (1)B−L symmetry breaking scale is around 1014 GeV, and all the supersymmetric particles except gravitino are around the TeV scale, while the gravitino mass is around 109-1010 GeV. Considering the complete potential terms linear in S, we for the first time show that the tadpole term, which is the key for such kind of inflationary models to be consistent with the observed scalar spectral index, vanishes after inflation. Thus, to obtain the μ term, we need to generate the supersymmetry breaking soft term AκS κ S due to AκS = 0 in no-scale supergravity, where and are vector-like Higgs fields at high energy. We show that the proper AκS κ S term can be obtained in the M-theory inspired no-scale supergravity. We also point out that AκS around 700 GeV can be generated via the renormalization group equation running from string scale. We briefly comment on the supersymmetry phenomenological consequences as well. It is well known that our Universe may experience an accelerated expansion, i.e., inflation [1-4], at a very early stage of evolution, as suggested by the observed temperature fluctuations in the cosmic microwave background radiation (CMB). From the particle physics point of view, supersym- - metry is the most promising extension for the Standard Model (SM). In particular, the scalar masses can be stabilized, and the superpotential is non-renormalized. Because gravity is also very important in the early Universe, it seems to us that supergravity theory is a natural framework for the inflationary model building [5, 6]. The F-term hybrid inflation in a supersymmetric high energy model with gauge symmetry G has a renormalizable superpotential W and a canonical Kähler potential K [7, 8]. In particular, the Z2 R-parity in the supersymmetric SMs (SSMs) is extended to a continuous U (1)R symmetry, which determines superpotential. With the minimal W and K , the gauge symmetry G is broken down to a subgroup H at the end of inflation. For the supersymmetric high energy model, in general, we can consider either a left–right model with gauge symmetry SU (3)C × SU (2)L × SU (2)R × U (1)B−L , or a Grand Unified Theory (GUT) such as the SU (5) model, the flipped SU (5) × U (1)X model, or the Pati–Salam SU (4)c × SU (2)L × SU (2)R model [9, 10]. H can be the SM or SM-like gauge group, etc. In the supersymmetric hybrid inflation [7],1 the quantum corrections arising from supersymmetry breaking drive inflation, and the scalar spectral index was predicted to be ns = 1 − 1/N 0.98, where N = 60 denotes the number of e-foldings necessary to resolve the horizon and flatness problems in Big Bang cosmology. Interestingly, with a class of linear supersymmetry breaking soft terms in the inflationary potential [14–18], such a kind of models can be highly consistent with the observed scalar spectral index values of 1 In the original papers on hybrid inflation [11,12] realized in super gravity, inflation ends when the GUT phase transition for symmetry breaking occurs, and the scalar power spectrum exhibits a slight blue tilt with ns > 1. For the supersymmetric hybrid inflation models considered in Refs. [7,13], the inflationary phase ends when the slow-roll conditions are violated before the phase transition, and a red-tilted spectral index of the density fluctuations ns = 1 − 1/N 0.98 is obtained. ns = 0.96 − 0.97 from the WMAP [19] and Planck satellite experiments [20,21] as well. In particular, the corresponding supersymmetry breaking A-term for the linear superpotential term can be around the TeV scale [14–18]. As we know, in the Minimal SSM (MSSM), there exists a well-known μ problem. However, the μHd Hu term is forbidden by U (1)R symmetry, where Hu and Hu are one pair of Higgs fields in the SSMs. With the linear supersymmetry breaking soft term after inflation, the inflaton field S acquires a Vacuum Expectation Value (VEV). Thus, the μ problem can be solved if there exists a superpotential term λS Hd Hu , as proposed by Dvali, Lazarides and Shafi (DLS) [22,23]. Assuming the minimal K , the magnitude of μ is typically around the gravitino mass mG [22,23]. Recently, such scenario has been studied in detail [13]. With the reheating and cosmological gravitino constraints, it was found that a consistent inflationary scenario gives rather concrete predictions reg (...truncated)


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Lina Wu, Shan Hu, Tianjun Li. No-scale \(\mu \) -term hybrid inflation, The European Physical Journal C, 2017, pp. 168, Volume 77, Issue 3, DOI: 10.1140/epjc/s10052-017-4741-9