Elementary Theorems Regarding Blue Isocurvature Perturbations

Understand

Blue CDM-photon isocurvature perturbations are attractive in terms of observability and may be typical from the perspective of generic mass relations in supergravity.

• We present and apply three theorems useful for blue isocurvature perturbations arising from linear spectator scalar fields.
• In the process, we give a more precise formula for the blue spectrum associated with the axion model of 0904.3800, which can in a parametric corner give a factor of O(10) correction.
• We explain how a conserved current associated with Peccei-Quinn symmetry plays a crucial role and explicitly plot several example spectra including the breaks in the spectra.