The PTOLEMY experiment (Princeton Tritium Observatory for Light, Early-Universe, Massive-Neutrino Yield) aims to achieve the sensitivity required to detect the relic neutrino background through a combination of a large area surface-deposition tritium target, MAC-E filter methods, cryogenic calorimetry, and RF tracking and time-of-flight systems. A small-scale prototype is in operation at the Princeton Plasma Physics Laboratory with the goal of validating the technologies that would enable the design of a 100 gram PTOLEMY. With precision calorimetry in the prototype setup, the limitations from quantum mechanical and Doppler broadening of the tritium target for different substrates will be measured, including graphene substrates. Beyond relic neutrino physics, sterile neutrinos contributing to the dark matter in the universe are allowed by current constraints on partial contributions to the number of active neutrino species in thermal equilibrium in the early universe. The current PTOLEMY prototype is expected to have unique sensitivity in the search for sterile neutrinos with electron-flavor content for masses of 0.1--1keV, where less stringent, 10eV, energy resolution is required. The search for sterile neutrinos with electron-flavor content with the 100g PTOLEMY is expected to reach the level $|U_{e4}|^2$ of $10^{-4}$--$10^{-6}$, depending on the sterile neutrino mass.
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