The precision of recent experiments such as ${\it Planck}$ have allowed us to constrain standard and non-standard physics (e.g., due to dark matter annihilation or varying fundamental constants) during the recombination epoch. However, we can also probe this era of cosmic history using model-independent variations of the free electron fraction, $X_{\rm e}$, which in turn affects the temperature and polarization anisotropies of the cosmic microwave background. In this paper, we improve on the previous efforts to construct and constrain these generalised perturbations in the ionization history, deriving new optimized eigenmodes based on the full Planck 2015 likelihood data, introducing the new module 'FEARec++'. We develop a direct likelihood sampling method for attaining the numerical derivatives of the standard and non-standard parameters, and discuss complications arising from the stability of the likelihood code. We improve the amplitude constraints of the ${\it Planck}$ 2015 principal components constructed here, $\mu_1=-0.09\pm0.12$, $\mu_2=-0.17\pm0.20$ and $\mu_3=-0.30\pm0.35$, finding no indication for departures from the standard recombination scenario. The third mode error is reduced by $60\%$. We utilise an efficient eigen-analyser that keeps the cross-correlations of the first three eigenmodes to $\xi_{\mu,\mu'}<0.1\%$ after marginalisation for all the considered data combinations. We also propose a new projection method for estimating constraints on the parameters of non-standard recombination. Using our eigenmodes, this allows us to recreate the ${\it Planck}$ constraint on the two-photon decay rate, $A_{\rm 2s1s}=7.60\pm0.64$, giving an estimate to within $\simeq 0.05\sigma$ of the full MCMC result. The improvements on the analysis using the ${\it Planck}$ data will allow us to implement this new method for analysis with fundamental constant variations in the future.

中文翻译：

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改进了对重组时代的模型独立约束和直接投影方法的发展

最近的实验（如 ${\it Planck}$）的精确度使我们能够在复合时代约束标准和非标准物理学（例如，由于暗物质湮灭或变化的基本常数）。然而，我们也可以使用自由电子分数 $X_{\rm e}$ 的独立于模型的变化来探索宇宙历史的这个时代，这反过来影响宇宙微波背景的温度和极化各向异性。在本文中，我们改进了之前在电离历史中构建和约束这些广义扰动的努力，基于完整的普朗克 2015 似然数据推导出新的优化特征模式，引入了新模块“FEARec++”。我们开发了一种直接似然采样方法来获得标准和非标准参数的数值导数，并讨论由似然码稳定性引起的并发症。我们改进了这里构建的 ${\it Planck}$ 2015 主成分的幅度约束，$\mu_1=-0.09\pm0.12$、$\mu_2=-0.17\pm0.20$ 和 $\mu_3=-0.30 \pm0.35$，没有发现偏离标准重组方案的迹象。第三模式误差减少$60\%$。我们利用一个高效的特征分析器，在对所有考虑的数据组合进行边缘化后，将前三个特征模式的互相关保持为 $\xi_{\mu,\mu'}<0.1\%$。我们还提出了一种新的投影方法，用于估计对非标准重组参数的约束。使用我们的本征模式，这允许我们重新创建对双光子衰减率的 ${\it Planck}$ 约束，$A_{\rm 2s1s}=7.60\pm0.64$，给出完整 MCMC 结果的估计值在 $\simeq 0.05\sigma$ 以内。使用 ${\it Planck}$ 数据进行分析的改进将使我们能够在未来实施这种具有基本常数变化的分析新方法。