No-Scale $\mu$-Term Hybrid Inflation

TL;DR

This paper introduces a novel no-scale supergravity model for $$-term hybrid inflation, achieving correct spectral index, tiny tensor-to-scalar ratio, and consistent supersymmetry breaking with TeV-scale particles and intermediate gravitino mass.

Contribution

It proposes the first $$-term hybrid inflation model within no-scale supergravity, addressing the tadpole term issue and linking inflation to supersymmetry breaking and M-theory.

Findings

Correct scalar spectral index $n_s$ obtained

Tensor-to-scalar ratio $r$ predicted to be extremely small (~$10^{-10}$-$10^{-8}$)

Supersymmetric particles at TeV scale with gravitino around $10^{9-10}$ GeV

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 $A^{S \Phi \Phi'}_{\kappa} \kappa S \Phi \Phi'$ 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.