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A variation of the fundamental constants is expected to affect thethermonuclear rates important for stellar nucleosynthesis. In particular,because of the very small resonant energies of Be8 and C12, the triple $\alpha$process is extremely sensitive to any such variations. Using a microscopicmodel for these nuclei, we derive the sensitivity of the Hoyle state to thenucleon-nucleon potential allowing for a change in the magnitude of the nuclearinteraction. We follow the evolution of 15 and 60 solar mass, zero metallicitystellar models, up to the end of core helium burning. These stars are assumedto be representative of the first, Population III stars. We derive limits onthe variation of the magnitude of the nuclear interaction and model dependentlimits on the variation of the fine structure constant based on the calculatedoxygen and carbon abundances resulting from helium burning. The requirementthat some C12 and O16 be present are the end of the helium burning phase allowsfor permille limits on the change of the nuclear interaction and limits oforder 10^{-5} on the fine structure constant relevant at a cosmologicalredshift of z ~ 15-20.

Effects of the variation of fundamental constants on Pop III stellar evolution