Curvature perturbations from kinetic preheating after $\alpha$-attractor inflation

Preheating at the end of inflation is a violent nonlinear process that efficiently transfers the energy of the inflaton to a second field, the preheat field. When the preheat field is light during inflation and its background value modulates the preheating process, the superhorizon isocurvature perturbations of the preheat field may be converted to curvature perturbations that leave an imprint on the cosmic microwave background and the large-scale structure of the universe. We use high-precision lattice simulations to study kinetic preheating after $\alpha$-attractor inflation, a case where the effective mass of the preheat field is naturally suppressed during inflation. By comparing the expansion e-folds between different Hubble patches, we find that the conversion from isocurvature perturbations to curvature perturbations is very inefficient and can hardly be detected by cosmological observations.