论文标题
分析自动差异性$λ$ CDM COSMography
Analytic auto-differentiable $Λ$CDM cosmography
论文作者
论文摘要
我介绍了标准$λ$ CDM宇宙学中距离计算的一般分析表达式（距离距离，时间坐标和吸收距离），从而允许存在辐射和非零曲率。该解决方案利用了椭圆积分的对称卡尔森基础，可以通过快速的数值算法对其进行评估，这些算法允许在GPU和自动差异上进行琐碎的并行化，而无需其他特殊功能。我在Phytorch.Cosmology软件包中引入了基于Pytorch的实现，并与数值集成和其他已知表达式（特殊情况）进行了简要检查其准确性和速度。最后，我展示了用于高维贝叶斯分析的应用程序，该应用程序通过距离计算利用自动分化来有效地为宇宙学参数的后代从最高$ 10^6 $模拟的IA型超级新星使用变量推断。
I present general analytic expressions for distance calculations (comoving distance, time coordinate, and absorption distance) in the standard $Λ$CDM cosmology, allowing for the presence of radiation and for non-zero curvature. The solutions utilise the symmetric Carlson basis of elliptic integrals, which can be evaluated with fast numerical algorithms that allow trivial parallelisation on GPUs and automatic differentiation without the need for additional special functions. I introduce a PyTorch-based implementation in the phytorch.cosmology package and briefly examine its accuracy and speed in comparison with numerical integration and other known expressions (for special cases). Finally, I demonstrate an application to high-dimensional Bayesian analysis that utilises automatic differentiation through the distance calculations to efficiently derive posteriors for cosmological parameters from up to $10^6$ mock type Ia supernovae using variational inference.
