Kavli Affiliate: Wayne Hu
| Summary:
If the Peccei-Quinn symmetry of an ultralight axion is broken before the end of inflation, axion quantum fluctuations seed isocurvature perturbations, linking them to the tensor-to-scalar ratio $r$. We extend the effective time average (ETA) approach of the Boltzmann code $rm AxiECAMB$ to accurately evolve these perturbations across the full axion mass range from dark energy ($m_a lesssim H_0$) to dark matter ($m_a gg 10^-28$ eV) types. We provide analytic fitting formulae for the axion abundance given the initial field value $φ_rm ini$, accurate at sub-percent level for $m_a gg H_0$ and allowed dark matter fraction $f_rm dm$. In the dark matter regime, the Planck bound on CDM isocurvature requires $r f_rm dm < 0.08,(m_a/10^-27,rm eV)^-1/2$, which becomes stronger than the current BICEP tensor bound for $m_a f_rm dm^2 gtrsim 10^-26.4,rm eV$. For $10^-32 lesssim m_a/rm eV lesssim 10^-28$, Jeans suppression breaks the degeneracy with CDM isocurvature, leaving unique signatures, and in the dark energy regime ($m_a lesssim H_0$), the isocurvature signal is even more highly suppressed, peaking only at the CMB quadrupole. We provide analytic scalings for both signatures. Given the tensor bound, any primary CMB detection in these two lightest regimes would indicate a non-inflationary origin of the isocurvature modes or a breakdown of the standard frozen-field misalignment scenario. A window of coexistence opens near $m_a sim 10^-25$ eV and $f_rm dm gtrsim 0.1$ where both axion isocurvature and tensor modes could be discovered just below current bounds while simultaneously alleviating the $S_8$ tension.
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