普朗克时代玻尔兹曼码的优化
Optimising Boltzmann codes for the Planck era
摘要：
高精度的测量宇宙微波背景（CMB）各向异性，可以预期从普朗克卫星，将需要高精度的理论预测。理论不确定性的一个可能来源是用于计算角功率谱的玻尔兹曼代码的输出中的数值误差。在这项工作中，我们进行了广泛的研究的公共玻尔兹曼代码CAMB的数值精度，并确定了一组参数，确定其输出的错误。我们表明，在当前的默认设置下，从未来的实验，如普朗克的数据中提取的宇宙学参数可以被标准的Lambda CDM模型的六个参数的标准偏差的十分之几，并可能更严重的扩展模型。我们执行一个优化程序，导致代码达到足够的精度，同时保持计算时间在合理的范围内。我们的结论是，数值误差对模型预测的理论不确定性的贡献得到了很好的控制--更准确地计算CMB光谱的主要挑战将是天体物理性质的。
英文摘要：
High precision measurements of the Cosmic Microwave Background (CMB) anisotropies, as can be expected from the Planck satellite, will require high-accuracy theoretical predictions as well. One possible source of theoretical uncertainty is the numerical error in the output of the Boltzmann codes used to calculate angular power spectra. In this work, we carry out an extensive study of the numerical accuracy of the public Boltzmann code CAMB, and identify a set of parameters which determine the error of its output. We show that at the current default settings, the cosmological parameters extracted from data of future experiments like Planck can be biased by several tenths of a standard deviation for the six parameters of the standard Lambda-CDM model, and potentially more seriously for extended models. We perform an optimisation procedure that leads the code to achieve sufficient precision while at the same time keeping the computation time within reasonable limits. Our conclusion is that the contribution of numerical errors to the theoretical uncertainty of model predictions is well under control -- the main challenges for more accurate calculations of CMB spectra will be of an astrophysical nature instead.
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