Abstract
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.
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