Bianchi Type I Space -Time Geometry of the Universe with Time Dependent G and $\Lambda$ 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 $a(t)={\left(sinhbt\right)}^{\frac{1}{n}}$ 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 $H_0=65.715Km/S/Mpc$ 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 $H_0=65.715\pm 2.392Km/S/Mpc$ 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.

26 pages, 7 figures