Cosmological Time Crystals from Gauss-Bonnet Gravity in Four Dimensions

We investigate various cosmological aspects of a 4-Dimensional Gauss-Bonnet Lagrangian, which is integrated into the Einstein Lagrangian with an arbitrary sign, using the Friedman-Lemaître-Robertson-Walker (FLRW) metric. We consider a general potential term, V(a), that depends on the scale factor a, and we analyze several scenarios by investigating the critical points of the dynamical equations and stability conditions to understand how the universe's behavior is affected by the Gauss-Bonnet term. Our research suggests that choosing the negative sign, this integration allows for the spontaneous breaking of time reflection symmetry. This can lead to the generation of a bounce universe even with a normal matter sector, marking a significant departure from traditional theories. Furthermore, we examine the possibility of a time-crystal universe, showing that under certain circumstances, the theory might give rise to cyclic universes.