Reinsch样条在宇宙学中的初步应用：用模拟OHD测定跃迁红移
Preliminary Application of Reinsch Splines to Cosmology: Transition Redshift Determination with Simulated OHD
摘要：
许多方案已经被提出来对宇宙动力学进行与模型无关的约束，例如非参数暗能量状态方程（EoS）ω（z）或减速参数q（z）。这些方法通常包含关于具有噪声的观测数据的导数过程。然而，它仍然是显着的不确定性时，人们估计的数值微分，特别是相应的截断误差。在这项工作中，我们介绍了一个整体的数值微分方法，首先制定的Reinsch（1967），这是光滑的三次样条函数。通过最小化泛函Φ（f）得到最优解。为了进一步研究该算法的潜力，我们将其应用于基于观测哈勃参数数据（OHD）的跃迁红移z_{t}的模拟膨胀率E（z）的估计。给出了确定Reinsch样条中自由参数S的一种有效方法。
英文摘要：
Many schemes have been proposed to perform a model-independent constraint on cosmological dynamics, such as nonparametric dark energy equation of state (EoS) ω(z) or the deceleration parameter q(z). These methods usually contain derivative processes with respect to observational data with noise. However, it still remains remarkably uncertain when one estimates the numerical differentiation, especially the corresponding truncation errors. In this work, we introduce a global numerical differentiation method, first formulated by Reinsch(1967), which is smoothed by cubic spline functions. The optimal solution is obtained by minimizing the functional Φ(f). To investigate the potential of the algorithm further, we apply it to the estimation of the transition redshift z_{t} with simulated expansion rate E(z) based on observational Hubble parameter data(OHD). An effective method to determine the free parameter S appearing in Reinsch Splines is provided.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
