Axion fluctuations generated during inflation lead to isocurvature and non-Gaussian temperature fluctuations in the cosmic microwave background radiation. Following a previous analysis for the model independent string axion we consider the consequences of a measurement of these fluctuations for two additional string axions. We do so independent of any cosmological assumptions. The first axion has been shown to solve the strong $CP$ problem for most compactifications of the heterotic string while the second axion, which does not solve the strong $CP$ problem, obeys a mass formula which is independent of the axion scale. We find that if gravitational waves interpreted as arising from inflation are observed by the PLANCK polarimetry experiment with a Hubble constant during inflation of $H_{\inf }\gtrsim {10}^{13}\mathrm{GeV}$ the existence of the first axion is ruled out and the second axion cannot obey the scale independent mass formula. In an appendix we quantitatively justify the often held assumption that temperature corrections to the zero temperature QCD axion mass may be ignored for temperatures $T\lesssim {\Lambda }_{\mathrm{QCD}}$.

• Received 1 February 2006

DOI:https://doi.org/10.1103/PhysRevD.73.123521