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We explore the cosmological sensitivity to the amplitude of isocurvaturefluctuations that would be caused by axions in the "anthropic window" where theaxion decay constant f_a >> 10^12 GeV and the initial misalignment angleTheta_i << 1. In a minimal Lambda-CDM cosmology extended with subdominantscale-invariant isocurvature fluctuations, existing data constrain theisocurvature fraction to alpha < 0.09 at 95% C.L. If no signal shows up, Planckcan improve this constraint to 0.042 while an ultimate CMB probe limited onlyby 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 off_a and H_I (Hubble parameter during inflation) we identify a small regionwhere axion detection remains within the reach of realistic cosmologicalprobes.

Isocurvature forecast in the anthropic axion window