A Study of Time Evolution of Some Cosmological Parameters in The Framework of an Anisotropic Kaluza-Klein Metric Using an Empirical Exponential Scale Factor

Abstract

The present study attempts to determine the time dependence of some cosmological parameters in flat space (i.e., a space of zero spatial curvature), in the framework of an anisotropic Kaluza-Klein metric. The field equations for this work have been derived from the metric by assuming a power-law relation between the normal scale factor and the scale factor corresponding to the extra (i.e., the fifth) dimension. An empirical scale factor, having the expression of a = B exp(αtβ), has been used here in order to derive the expressions for some cosmological parameters as functions of time. The reason for choosing this scale factor is that it generates an expression for the deceleration parameter which undergoes a change of sign, as time goes on, from positive to negative, indicating a transition of the universe from an initial state of decelerated expansion to that of an accelerated expansion (which is its present state), as has been inferred from astrophysical observations. We have graphically depicted the evolution of some cosmological parameters with respect to what one may call the relative time, expressed as t/t0, where t0 is the present age of the universe. The present study finds the dynamical cosmological constant (Λ) to be negative, and it becomes less negative with time, changing at a gradually decreasing rate. The dependence of pressure of the all-pervading cosmic fluid upon density, corresponding to the fifth dimension, has been described in terms of a skewness parameter (δ) which comes out to be decreasing with time. The anisotropy factor has been calculated in this study, whose numerical value has been found to be decreasing with time, indicating a journey of the universe towards phases of gradually smaller anisotropy.