Lambert W宇宙流体模型H(z)公式的解析积分
Analytic Integration of the Lambert W Cosmic Fluid Model H(z) Formula
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中文总结 AI 辅助
本文推导了2026年初Dubey等人提出的Lambert W宇宙流体模型H(z)公式的解析积分，替代其原数值积分形式，便于该模型的相关研究探索。
中文摘要 AI 辅助
Lambert W（LW）宇宙流体状态方程模型由S. Saha和K. Bamba于2019-2020年提出。2026年初Dubey等人的一篇论文对LW模型进行了观测数据拟合以估算模型参数，该论文给出了红移z处相对哈勃因子对数ln(H(z)/H₀)的公式，其基于数值积分。该积分可解析求解，本文在工作论文中给出了详细推导，所得H(z)/H₀的解析表达式便于探索LW模型。
英文摘要
The Lambert $W$ (LW) model for the cosmic fluid equation of state was proposed by S. Saha and K. Bamba in 2019-2020. A recent (early 2026) paper by Dubey, et al, carries out a new fit of the LW model to observational data, in order to estimate the model's parameters. That paper exhibits a formula for the logarithm of the relative Hubble factor at redshift $z$, $\ln(H(z)/H_0)$, which is based upon a numerical integration. That integral can be evaluated analytically, and we present the details in this working paper. The resulting analytic expression for $H(z)/H_0$ may be convenient for exploration of the LW model. We present two approximation formulas for the Lambert $W$ function, highly accurate for redshifts $z$ between 0 and 3, which may be useful for researchers who do not have ready access to a function library with the Lambert $W$ function. We also present a simplified proof of the analytic formula for another logarithmic integral which may be useful for exploring some variants of the LW model.
发表机构
- Western University（韦仕敦大学）
- Universidad Simón Bolívar（西蒙玻利瓦尔大学）
- Panihati Mahavidyalaya（帕尼哈蒂学院）
- King’s University College, Western University（韦仕敦大学金斯大学学院）
机构由 AI 辅助整理，请以论文原文为准。
