The proposal is to measure the low-energy spin dynamics of the ferromagnetic superconductor UGe2 at the pressure which maximizes superconducting transition temperature and at which the first-order transition between two different moment values in the ferromagnetic states is driven to a critical end point. The experiment will mark a technical milestone, demonstrating how low-energy inelastic neutron scattering measurements may be made on pressurized samples to study new physics of the correlated electrons and will open the way for future studies in many other topical quantum critical systems.