Update of axion CDM energy density

TL;DR

The paper refines the axion cold dark matter relic density by incorporating updated current-quark masses, a temperature‑dependent axion mass through instanton dynamics, and anharmonic effects treated via an adiabatic invariant. It also analyzes how the QCD chiral phase transition, modeled with a bag picture, could affect axion number and entropy, finding the effect is minimal for most of the parameter space. The authors derive a corrected relic-density formula that includes an initial overshoot correction and an anharmonic correction function, leading to a bound Fa ≤ 10^12 GeV for θ1 ~ O(1) and allowing Fa ≳ 10^13 GeV for small misalignment angles. These results tighten the axion parameter space for CDM and highlight the influence of QCD thermodynamics and quark masses on cosmological axion abundance.

Abstract

We improve the estimate of the axion CDM energy density by considering the new values of current quark masses, the QCD phase transition effect and a possible anharmonic effect.

Figures (9)

• Figure 1: The phase transition near the critical temperature $T_{\rm c}\approx 150$ MeV. The solid line describes a smooth path first order transition and the dashed line describes a supercooling case.
• Figure 2: The determinental interaction of light quarks.
• Figure 3: The correction factor from anharmonic effect.
• Figure 4: The solid curves represent the $\theta$ evolution for $\theta_1=0.1$ (in the upper figure) and $\theta_1=3$ (in the lower figure). The common tangents to the dashed curves are the square root of the invariant $\sqrt{I}$. After a half period, they almost approach to the condition $H\ll m_a$.
• Figure 5: The initial correction factors $f_2$ and $f_3$.