  In this study, the mechanism of particle creation using varying gravitational
and cosmological constants and deceleration parameter has been studied for
Friedman-Robertson-Walker at high dimensions to explain early deceleration and
present accelerating phases. In order to investigate the dynamics of two
phases, we have considered two different ansatz for the scale factor of the
form $a(t)=\sqrt{t^{\alpha}e^{t}}$ and $a(t)=\sqrt{\sin h(kt)}$ which are
general form of power-law expansions. Firstly we modified $d$-dimensional field
equations depend on time introduce a general formulation of particle creation
and entropy generation mechanisms. We investigate time dependence of the
several cosmological constant and quantities such as particle creation $\psi$
and entropy $S$, gravitational constant $G$, cosmological term $\Lambda$,
energy density $\rho$, deceleration parameter $q$ etc. It is shown that all
constant and other quantities, except the cosmological constant $G$ and entropy
$S$, characteristically decrease with time for two scale factors in all
dimensions. However, the cosmological constant $G$ and entropy $S$ increase
with time. Additionally, it is shown that the cosmological constant $\Lambda$
is unexpectedly independent of particle creation mechanism.
