JCAP, 06, 002 (2024)

Cosmological time crystals from Gauss-Bonnet gravity in four dimensions

H. Khodabakhshi¹, F. Shojai² and Hong Lü^1,3

1 Center for Joint Quantum Studies, Department of Physics, School of Science, Tianjin University, Tianjin 300350, China.

2 Department of Physics, University of Tehran, P.O. Box 14395-547, Tehran, Iran.

3 Joint School of National University of Singapore and Tianjin University, International Campus of Tianjin University, Binhai New City, Fuzhou 350207, China.

* h_khodabakhshi@tju.edu.cn, fshojai@ut.ac.ir, mrhonglu@gmail.com

Abstract

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 wall-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.