Time evolution of an anisotropic universe under Kaluza-Klein framework with a dynamical cosmological constant (International Journal of Mathematics and Physics, 2024)
The objective of the present study is to determine the time evolution of the universe with zero spatial curvature, under Kaluza-Klein framework, in the presence of an anisotropic fluid. To derive the field equations, we have used a power law relation between the normal scale factor and the extra-dimension scale factor. Time-variation of cosmological quantities depends upon the parameter that connects these scale factors. Using an ansatz for a hybrid scale factor (i.e., a = tαeβt) we have derived expressions for various cosmological parameters in terms of cosmic time and depicted their time dependence graphically. The dynamical cosmological term (Λ) varies extremely slowly at the present time, indicating a slow change in the dark energy content of the universe which is held responsible for cosmic acceleration. The pressure associated with the fifth dimension has been expressed in terms of a skewness parameter (δ). Its behaviour shows that the present universe has a small anisotropy and it becomes smaller with time. This observation is consistent with the behaviour of the anisotropy factor which decreases with time.