Higher Dimensional Dust Cosmological Implications of a Decay Law for $Λ$ Term : Expressions for Some Observable Quantities
In this paper we have considered the multidimensional cosmological implications of a decay law for $Λ$ term that is proportional to $β\frac{\ddot {a}}{a}$, where $β$ is a constant and $a$ is the scale factor of RW-space time. We discuss the cosmological consequences of a model for the vanishing pressure for the case $k=0$. It has been observed that such models are compatible with the result of recent observations and cosmological term $Λ$ gradually reduces as the universe expands. In this model $Λ$ varies as the inverse square of time, which matches its natural units. The proper distance, the luminosity distance-redshift, the angular diameter distance-redshift, and look back time-redshift for the model are presented in the frame work of higher dimensional space time. The model of the Freese {\it et al.} ({\it Nucl. Phys. B} {\bf 287}, 797 (1987)) for $n=2$ is retrieved for the particular choice of $A_{0}$ and also Einstein-de Sitter model is obtained for $A_{0} = {2/3}$. This work has thus generalized to higher dimensions the well-know result in four dimensional space time. It is found that there may be significant difference in principle at least, from the analogous situation in four dimensional space time.