  We explore the cosmological sensitivity to the amplitude of isocurvature
fluctuations that would be caused by axions in the "anthropic window" where the
axion decay constant f_a >> 10^12 GeV and the initial misalignment angle
Theta_i << 1. In a minimal Lambda-CDM cosmology extended with subdominant
scale-invariant isocurvature fluctuations, existing data constrain the
isocurvature fraction to alpha < 0.09 at 95% C.L. If no signal shows up, Planck
can improve this constraint to 0.042 while an ultimate CMB probe limited only
by cosmic variance in both temperature and E-polarisation can reach 0.017,
about a factor of five better than the current limit. In the parameter space of
f_a and H_I (Hubble parameter during inflation) we identify a small region
where axion detection remains within the reach of realistic cosmological
probes.
