广义相对论框架下含随时间变化的G和$\Lambda$的宇宙Bianchi I型时空几何：观测方面
Bianchi Type I Space -Time Geometry of the Universe with Time Dependent G and $Λ$ Within the Framework of General Relativity: Observational Aspects
- Laxminarayan Innovation Technological University（拉克什米纳拉扬创新理工大学）
- S. B. Jain Institute of Technology, Management and Research（S.B. 贾因技术、管理与研究院）
- Visvesvaraya National Institute of Technology（维斯瓦纳塔国家理工学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究基于广义相对论，采用Bianchi I型时空与双曲尺度因子构建含时变G和$\Lambda$的宇宙模型，通过观测数据约束参数，验证其与宇宙加速膨胀及减速-加速转变的一致性。
AI中文摘要：
受寻找可接受宇宙学模型的最新进展启发，本文致力于探索一种具有初始各向异性且加速演化、最终达到各向同性特征的宇宙数学模型。我们采用了被广泛认可的各向异性Bianchi I型宇宙时空几何，以探索物理上可行的模型。为得到可接受的模型，我们对尺度因子采用双曲形式$ a(t)= \left( sinh bt \right)^{\frac{1}{n}} $，并采用关系$ \Lambda=\Lambda_0 \frac{\ddot{a}}{a}$。模型参数通过$\chi^2$最小化技术进行约束。利用35个CC测量数据，我们得到当前膨胀率$H_0= 65.715 Km/S/Mpc$，以及$n= 1.3024$。为进一步估计最佳拟合参数的局部不确定性，我们从归一化残差的雅可比矩阵计算协方差。对应的1$\sigma$不确定性为$ H_0=65.715 \pm 2.392 Km/S/Mpc$，$n= 1.3024 \pm 0.0842$。通过宇宙学参数的图形表示，我们讨论了当前模型的物理和动力学行为。研究发现，膨胀历史的观测约束与当前加速阶段以及中间红移处从减速到加速的转变一致。我们还在所采用的模型内研究了推导得到的宇宙学量的相应演化过程。
英文摘要：
Inspired by the latest progress in the hunt of acceptable cosmological model of the universe, present paper is devoted to explore a mathematical model of the universe having initial anisotropy and with accelerated evolution that attains isotropic character. We have considered a widely accepted anisotropic Bianchi type I space-time geometry of the universe to explore a physically viable model. To find an acceptable model, we adopted a hyperbolic form for the scale factor as $ a(t)= \left( sinh bt \right)^{\frac{1}{n}} $ and a relation $ Λ=Λ_0 \frac{\ddot{a}}{a}$. The model parameters are constrained by $ χ^2$ minimization techniques. Using 35 CC measurements we obtain present day expansion rate $H_0= 65.715 Km/S/Mpc$ and the value of $ n= 1.3024$. Further to estimate the local uncertainties of the best fit parameter, we calculate covariance from the Jacobin of the normalized residuals. The corresponding 1 $σ$ uncertainties are $ H_0=65.715 \pm 2.392 Km/S/Mpc$ and $n= 1.3024 \pm 0.0842$. The physical and dynamical behaviour of present model has been discussed by a graphical representation of cosmological parameters. The observational constraints on the expansion history are found to be consistent with a present accelerated phase and a transition from deceleration to acceleration at an intermediate redshift. The corresponding evolution of the derived cosmological quantities is also investigated within the adopted model.
