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Ultralight axions (ma=10-18 eV), motivated by string theory, can be a powerful probe of the energy scale of inflation. Here it is shown that in contrast to heavier axions the isocurvature modes in the ultralight axions can coexist with observable gravitational waves. Large-scale structure constraints severely limit the parameter space for axion mass, density fraction, and isocurvature amplitude. It is also shown that radically different cosmic microwave background observables for the ultralight axion isocurvature mode additionally reduce this space. The results of a new, accurate, and efficient method to calculate this isocurvature power spectrum are presented and can be used to constrain ultralight axions and inflation [ABSTRACT FROM AUTHOR]