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arXiv · 2609.00030

Bianchi Type I Space -Time Geometry of the Universe with Time Dependent G and $\Lambda$ Within the Framework of General Relativity: Observational Aspects

S. Kotambkar·G. K. Goswami·R. Kelkar·G. P. Singh
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Abstract

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 $ \Lambda=\Lambda_0 \frac{\ddot{a}}{a}$. The model parameters are constrained by $ \chi^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 $\sigma$ 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.

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S. Kotambkar, G. K. Goswami, R. Kelkar, G. P. Singh. 2026-08-28. Bianchi Type I Space -Time Geometry of the Universe with Time Dependent G and $\Lambda$ Within the Framework of General Relativity: Observational Aspects. https://arxiv.org/abs/2609.00030

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