Understand
Incorporating the QCD axion and simultaneously satisfying current constraints on the dark matter density and isocurvature fluctuations requires non-minimal fine-tuning of inflationary parameters or the axion misalignment angle (or both) for Peccei-Quinn symmetry-breaking scales $f_a > 10^{12}$ GeV.
- To gauge the degree of tuning in models with many axion-like fields at similar symmetry-breaking scales and masses, as may occur in string theoretic models that include a QCD axion, we introduce a figure of merit ${\cal F}$ that measures the fractional volume of allowed parameter space: the product of the slow roll parameter $\epsilon$ and each of the axion misalignment angles, $\theta_0$.
- For a single axion, $\mathcal{F} \lesssim 10^{-11}$ is needed to avoid conflict with observations.
- We show that the fine tuning of $\mathcal{F}$ becomes exponentially more extreme in the case of numerous axion-like fields.
Reading the bibliography…