No-Scale $\mu$-Term Hybrid Inflation

Abstract

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 prediced 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 TeV scale while gravitino mass is around $10^{9-10}$ 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 $A_{\kappa }^{S\Phi {\Phi }^{\prime }}\kappa S\Phi {\Phi }^{\prime }$ due to $A_{\kappa }^{S\Phi {\Phi }^{\prime }}=0$ in no-scale supergravity, where $\Phi$ and ${\Phi }^{\prime }$ are vector-like Higgs fields at high energy. We show that the proper $A_{\kappa }^{S\Phi {\Phi }^{\prime }}\kappa S\Phi {\Phi }^{\prime }$ term can be obtained in the M-theory inspired no-scale supergravity. We also point out that $A_{\kappa }^{S\Phi {\Phi }^{\prime }}$ around 700 GeV can be generated via the renormalization group equation running from string scale.

15 pages, 4 figures; v2: references added

References in corpus (8)

• Anatomy of F_D-Term Hybrid Inflation
• Solving the $\eta$-Problem in Hybrid Inflation with Heisenberg Symmetry and Stabilized Modulus
• Resurrecting No-Scale Supergravity Phenomenology
• Hybrid Inflation in the Complex Plane
• The Golden Point of No-Scale and No-Parameter $\mathcal{F}$-SU(5)
• Observable Gravity Waves From Supersymmetric Hybrid Inflation
• Confronting Electroweak Fine-tuning with No-Scale Supergravity
• The Super-Natural Supersymmetry and Its Classic Example: M-Theory Inspired NMSSM

Cited by in corpus (11)

• Gravitational Waves and Primordial Black Holes from Supersymmetric Hybrid Inflation
• Shifted $\mu$-hybrid inflation, gravitino dark matter, and observable gravity waves
• $\mu$-Hybrid Inflation with Low Reheat Temperature and Observable Gravity Waves
• Inflation from a No-scale supersymmetric $SU(4{)}_c\times SU(2{)}_L\times SU(2{)}_R$ model
• PeV-Scale SUSY and Cosmic Strings from F-term Hybrid Inflation
• Probing the Supersymmetry-Mass Scale With F-term Hybrid Inflation
• Realistic Inflation in No-Scale $U(1{)}_R$ Symmetric Flipped $SU(5)$
• $\mu$-Hybrid Inflation and Metastable Cosmic Strings in $\mathbf{SU}(3{)}_{\mathbf{c}}\times \mathbf{SU}(2{)}_{\mathbf{L}}\times \mathbf{SU}(2{)}_{\mathbf{R}}\times \mathbf{U}(1{)}_{\mathbf{B}-\mathbf{L}}$
• Analytical study of classic models of Hybrid Inflation
• A note on supergravity inflation in braneworld
• Development of generic no-scale inflation