Split supersymmetry and hybrid inflation in light of Atacama Cosmology Telescope DR6 data

Abstract

Inspired by the recent measurement of the scalar spectral index, $n_s=0.9743\pm 0.0034$, by the Atacama Cosmology Telescope (ACT) DR6 data, we present an update on the split supersymmetry hybrid inflation model, also known as $\mu$-term hybrid inflation. The model employs a canonical Kähler potential but incorporates an additional renormalizable term in the superpotential $W$, which yields the MSSM $\mu$-term following supersymmetry breaking. This additional term in $W$ is responsible for a high reheat temperature, $T_r\gtrsim 10^{12}$ GeV, and consequently the necessity of split supersymmetry in this class of models. The predicted scalar spectral index is in excellent agreement with the ACT measurement and $r$, the tensor to scalar ratio, is estimated to be less than or of order $10^{-2}-10^{-3}$. For the running of the scalar spectral index we find $|d{n}_s/d\ln k|=O(10^{-4})$. With $T_r\gtrsim 10^{12}$ GeV, leptogenesis is readily implemented in this class of models. A wino-like LSP with mass of around 2 TeV is a plausible dark matter candidate.

Comments: 12 pages, 5 figures