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We examine thermal warm dark matter (WDM) models that are being probed bycurrent constraints, and the relationship between the particle dark matter spinand commensurate thermal history. We find significant corrections to the linearmatter power spectrum for given thermal WDM particle masses. Two primaryclasses are examined: spin-1/2 particles (e.g., thermalized sterile neutrinos,axinos) and thermal spin-3/2 particles (e.g., gravitinos or non-supersymmetricparticles). We present new transfer function fits for thermal WDM candidates inparticle mass regimes beyond the range of previous work, and at the scales ofcurrent and upcoming constraints. Importantly, we find that the standard,predominantly used, spin-1/2, thermal WDM particle produces a colder transferfunction than that determined in previous work. We also analyze the entropyrequirements for these WDM models to successfully produce observed dark matterdensities. We explore the early Universe physics of gravitinos as eitherpartially thermalized or fully thermalized species, which considerably changesthe particle dark matter candidates' thermalization history and effects onstructure formation. For the first time, we also calculate the transferfunction for thermal spin-3/2 WDM.

Entering the Era of Measuring Sub-Galactic Dark Matter Structure:  Accurate Transfer Functions for Axino, Gravitino & Sterile Neutrino Thermal  Warm Dark Matter