The naturalness problem of PQ symmetry motivates study of the heavy QCD axion, with masses m_a > 1 MeV generated at scales above the QCD scale, and low values of the PQ symmetry breaking scale, f_a. We compute the abundance of such axions in a model-independent way, assuming only that they freeze-out after reheating from inflation, and are not subsequently diluted by new physics. If these axions decay between neutrino decoupling and the last scatter era of the Cosmic Microwave Background (CMB), they dilute the neutrinos and their abundance is constrained by CMB measurements of the energy density in dark radiation, N_eff. We accurately compute this bound using a numerical code to evolve the axion momentum distribution, including many key processes and effects previously ignored. We assume that the only relevant axion decays are to final states involving Standard Model particles. We determine regions of (m_a, f_a) that will give a signal in N_eff at CMB Stage 4 experiments. We similarly compute the N_eff bound and CMB Stage 4 signal for heavy axions that can decay to light mirror photons. Finally, we compute the bounds on heavy axions with mass below 1 MeV that decay after the era of CMB last scatter, from their contribution to cold or hot dark matter or N_eff at this era.

PQ 对称性的自然性问题激发了对重 QCD 轴子的研究，在 QCD 尺度以上的尺度上产生质量m _a > 1 MeV，并且 PQ 对称破缺尺度f _a的值较低。我们以与模型无关的方式计算此类轴子的丰度，仅假设它们在因膨胀而重新加热后冻结，并且随后不会被新物理学稀释。如果这些轴子在中微子解耦和宇宙微波背景 (CMB) 最后散射时代之间衰变，它们会稀释中微子，并且它们的丰度受到 CMB 暗辐射能量密度测量N _eff的限制。我们使用数字代码精确计算这个界限，以演化轴子动量分布，包括许多以前忽略的关键过程和效应。我们假设唯一相关的轴子衰变是涉及标准模型粒子的最终状态。我们确定 ( m _a , f _a )区域将在 CMB 第 4 阶段实验中在N _eff中发出信号。我们同样计算可以衰减为光镜面光子的重轴子的N _eff边界和 CMB 第 4 阶段信号。最后，我们计算了质量低于 1 MeV 的重轴子的界限，这些重轴子在 CMB 最后一次散射时代之后衰变，根据它们在这个时代对冷或热暗物质或N _{eff的贡献。}