Bianchi Type I Space -Time Geometry of the Universe with Time Dependent G and Λ Within the Framework of General Relativity: Observational Aspects
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 $ 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 H0= 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 ± 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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BibTeX
@misc{kotambkar2026bianchi,
title = {{Bianchi Type I Space -Time Geometry of the Universe with Time Dependent G and $Λ$ Within the Framework of General Relativity: Observational Aspects}},
author = {S. Kotambkar and G. K. Goswami and R. Kelkar and G. P. Singh},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00030},
eprint = {2609.00030},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00030},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bianchi Type I Space -Time Geometry of the Universe with Time Dependent G and Λ Within the Framework of General Relativity: Observational Aspects
AU - S. Kotambkar
AU - G. K. Goswami
AU - R. Kelkar
AU - G. P. Singh
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.00030
UR - https://arxiv.org/abs/2609.00030
AB - 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 ± 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.
ER -