Adiabatic invariant approach on Friedmann cyclic universe

Oscillating or cyclic models of the universe were inspired by Friedmann's seminal paper of 1922. The model supposes a closed universe. In this work, we study Friedmann closed universe using the adiabatic invariant approach. We start revisiting the cosmological force proposed by N. Rosen and derive the Lagrangian density from Rosen's concepts of cosmological force. Importantly, we introduce the Noether gauge symmetry followed by the Rund-Traumann identity (RTI) and adiabatic invariant approach to examine the cyclic models. We consider a single component form of relativistic matter (stiff matter) at $a(t=0)$ and $a(t=T)$, and surprisingly discover the world period is given by $\sim 15.8$ Gy which is very close to that computed using the Friedmann's formula for the cyclic universe.