利用高斯过程重建暗能量和膨胀动力学
Reconstruction of dark energy and expansion dynamics using Gaussian processes
摘要：
直接从观测数据重建有效的暗能量状态方程是宇宙学中的一个重要问题。由于物理模型很少，未来的暗能量研究不能仅仅基于约束暗能量参数空间，因为发现的误差强烈依赖于所考虑的参数化。我们提出了一种新的非参数方法，使用高斯过程重建膨胀率和暗能量的历史，这是一种用于平滑数据的完全贝叶斯方法。我们提出了一个教学介绍高斯过程，并讨论如何可以用它来鲁棒地区分数据在一个合适的方式。利用这种方法，我们证明了暗能量巡天-超新星巡天（DES）可以精确地恢复一个缓慢演化的状态方程，在z=0时σ_w = +-0.04（95%CL），在z=0.7时σ_w = +-0.2，在z~0.14的最佳点处误差最小为+-0.015，只要模型的其他参数是已知的。膨胀历史的误差要小一个数量级，但对暗能量没有任何假设。使用高斯过程计算函数及其前三阶导数的代码已经开发出来，可在http://www.acgc.uct.ac.za/~seikel/GAPP/index.html下载。
英文摘要：
An important issue in cosmology is reconstructing the effective dark energy equation of state directly from observations. With few physically motivated models, future dark energy studies cannot only be based on constraining a dark energy parameter space, as the errors found depend strongly on the parameterisation considered. We present a new non-parametric approach to reconstructing the history of the expansion rate and dark energy using Gaussian Processes, which is a fully Bayesian approach for smoothing data. We present a pedagogical introduction to Gaussian Processes, and discuss how it can be used to robustly differentiate data in a suitable way. Using this method we show that the Dark Energy Survey - Supernova Survey (DES) can accurately recover a slowly evolving equation of state to sigma_w = +-0.04 (95% CL) at z=0 and +-0.2 at z=0.7, with a minimum error of +-0.015 at the sweet-spot at z~0.14, provided the other parameters of the model are known. Errors on the expansion history are an order of magnitude smaller, yet make no assumptions about dark energy whatsoever. A code for calculating functions and their first three derivatives using Gaussian processes has been developed and is available for download at http://www.acgc.uct.ac.za/~seikel/GAPP/index.html .
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