Primordial black holes and scalar-induced gravitational waves in sneutrino hybrid inflation

We investigate the possibility that primordial black holes (PBHs) can be formed from large curvature perturbations generated during the waterfall phase transition in a supersymmetric scenario where sneutrino is the inflaton in a hybrid inflationary framework. We obtain a spectral index (${n}_{s}\ensuremath{\simeq}0.966$), and a tensor-to-scalar ratio ($r\ensuremath{\simeq}0.0056--{10}^{\ensuremath{-}11}$), consistent with the current Planck data satisfying PBH as dark matter (DM) and detectable gravitational wave (GW) signal. Our findings show that the mass of PBH and the peak in the GW spectrum is correlated with the right-handed (s)neutrino mass. We identify parameter space where PBHs can be the entire DM candidate of the Universe (with mass ${10}^{\ensuremath{-}13}{M}_{\ensuremath{\bigodot}}$) or a fraction of it. This can be tested in future observatories, for example, with amplitude ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{GW}}{h}^{2}\ensuremath{\sim}{10}^{\ensuremath{-}9}$ and peak frequency $f\ensuremath{\sim}0.1\text{ }\text{ }\mathrm{Hz}$ in LISA and ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{GW}}{h}^{2}\ensuremath{\sim}{10}^{\ensuremath{-}11}$ and peak frequency of $\ensuremath{\sim}10\text{ }\text{ }\mathrm{Hz}$ in Einstein Telescope via second-order GW signals. We study two models of sneutrino inflation: Model-1 involves the canonical sneutrino kinetic term, which predicts the sub-Planckian mass parameter $M$, while the coupling between a gauge singlet and the waterfall field, $\ensuremath{\beta}$, needs to be quite large whereas, for the model-2 involving the $\ensuremath{\alpha}$-attractor canonical sneutrino kinetic term, $\ensuremath{\beta}$ can take a natural value. Estimating explicitly, we show that both models have mild fine-tuning. We also derive an analytical expression for the power spectrum in terms of the microphysics parameters of the model like (s)neutrino mass, etc. that fits well with the numerical results. The typical reheat temperature for both the models is around ${10}^{7}--{10}^{8}\text{ }\text{ }\mathrm{GeV}$ suitable for nonthermal leptogenesis.