标题： 观测约束与具有二次状态方程的暗能量 显示英文标题

标题： Observational Constraints on the Dark Energy with a Quadratic Equation of State

摘要： 在本研究中，我们引入了一个具有二次状态方程（EoS）的新型晚期有效暗能量模型，并严格检验其观测约束。 最初，我们深入研究了该模型的背景动力学，追踪线性阶次的扰动演化。 我们的方法涉及用一种动态有效的暗能量流体替代传统的宇宙学常数。 利用涵盖Planck 2018宇宙微波背景（CMB）、Ia型超新星（SNe）、重子声学振荡（BAO）以及对哈勃常数$H_0$ （R21）的先验的多样化观测数据集，我们限制了模型参数。 我们通过将红移函数的哈勃参数与观测哈勃数据（OHD）进行比较，验证了模型的一致性，并将其性能与标准$\Lambda$CDM 模型进行基准比较。 此外，我们的研究通过计算宇宙学参数如减速度参数、相对哈勃参数和哈勃率的演化，探讨了该模型的动力学行为。 此外，采用贝叶斯分析，我们确定了所提出模型与参考$\Lambda$CDM 模型相比的贝叶斯证据。 尽管我们的分析揭示了该模型在各种观测测试中的良好行为，但当探索完整数据集组合时，众所周知的宇宙学张力仍然存在。 显示英文摘要

摘要： In this study, we introduce a novel late-time effective dark energy model characterized by a quadratic equation of state (EoS) and rigorously examine its observational constraints. Initially, we delve into the background dynamics of this model, tracing the evolution of fluctuations in linear order. Our approach involves substituting the conventional cosmological constant with a dynamically effective dark energy fluid. Leveraging a diverse array of observational datasets encompassing the Planck 2018 Cosmic Microwave Background (CMB), Type Ia Supernovae (SNe), Baryon Acoustic Oscillations (BAO), and a prior on the Hubble constant $H_0$ (R21), we constrain the model parameters. We establish the model's consistency by comparing the Hubble parameter as a function of redshift against observational Hubble data (OHD), benchmarking its performance against the Standard $\Lambda$CDM model. Additionally, our investigation delves into studies of the model's dynamical behavior by computing cosmological parameters such as the deceleration parameter, relative Hubble parameter, and the evolution of the Hubble rate. Furthermore, employing Bayesian analysis, we determine the Bayesian Evidence for our proposed model compared to the reference $\Lambda$CDM model. While our analysis unveils the favorable behavior of the model in various observational tests, the well-known cosmological tensions persist when the full dataset combination is explored.