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 $H_0= 65.715 Km/S/Mpc$ 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.