  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
except for the axions being massless during inflation. 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 \apprge 10^13 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
\apprle \Lambda_QCD.
