Document Type : Original Article

Authors

• A Sarfaraz ¹
• M Siddique ²

¹ Department of Mathematics, Division of Science and Technology, University of Education Lahore, Pakistan

² Department of Mathematics, Riphah International University, Faisalabad Campus, Pakistan

Abstract

Two dark energy models $\Lambda \sim (\frac{\dot{a}}{a})^{2}$ and $\Lambda \sim \frac{\ddot{a}}{a}$ are studied by taking into account the gravitational constant G is a time-dependent parameter in the framework of Chern-Simons modified gravity. It is found that the gravitational constant shown the increasing behavior proportional to those of the time parameter for each model. These models are compared with observational results by regulating the values of the parameters. Our investigations indicated that the model $\Lambda \sim (\frac{\dot{a}}{a})^{2}$ is generally attractive in nature while the other model $\Lambda \sim \frac{\ddot{a}}{a}$ coincides to repulsive situation and consequently match with the current scenario of the accelerating universe. We calculated the variation of G(t) which showed that it changes rapidly when the value of $\omega$ is taken between the limit $-1.33 <\omega< -0.79 $. It is viewed that due to the composite influence of time-variable $\Lambda$ and G(t), the universe expanded with acceleration. Further, it is estimated that  the range for variation of G(t) with  proper tuning of parameters $\alpha$ and $\beta$ is given as $-(1.89\pm 0.10)\times 10^{-11}yr^{-1}<\frac{\dot{G}}{G}<0$ which match with Ia type supernova.

Keywords

• Dynamical CS Modified Gravity
• Dark Energy
• Gravitational constant