  In this work a new law of varying deceleration parameter of third degree have
been proposed. The solutions of the modified field equations have been derived
under the newly proposed law of the deceleration parameter. Model exhibits the
Big-bang singularity at cosmic time ($t=0$) and shows Big Rip at ($t=n$) then
it re-enter the phase of initial singularity at $t=2n$ and ends its cyclic
behavior at $t=3n$. The evolution of the physical and dynamical parameters of
the Universe have been studied and the graphical representation has also been
shown. Further $Om(z)$ diagnostic parameter and the energy conditions have also
been studied together with their graphical representations.
