# Gravity Waves, Axion and Gravitino Dark Matter in $μ$-Hybrid Inflation [CL]

We propose a novel reformulation of supersymmetric (more precisely $\mu$-) hybrid inflation based on a U(1) or any suitable extension of the minimal supersymmetric standard model (MSSM) which also resolves the $\mu$ problem. For a U(1) extension discussed here the symmetry can be either local or global and includes the axion case. We employ a suitable Kahler potential which effectively yields quartic inflation with non-minimal coupling to gravity. Imposing the gravitino Big Bang Nucleosynthesis (BBN) constraint on the reheat temperature ($T_r \lesssim 10^6$ GeV) and requiring a neutralino LSP, the tensor to scalar ratio ($r$) has a lower bound $r \gtrsim 0.003$. The U(1) symmetry breaking scale lies between $10^6$ and $10^{13}$ GeV. For the axion case with a decay constant $f_a = 10^{11}-10^{12}$ GeV, the isocurvature fluctuations are adequately suppressed and $r \geq 0.007-0.02$. We also discuss a scenario with gravitino dark matter with its mass estimated to lie between $0.3$ to $3$ GeV.