  By including appropriate Riemman cubic invariants, we find that the dynamics
of classical time crystals can be straightforwardly realized in Einstein
gravity on the FLRW metric. The time reflection symmetry is spontaneously
broken in the two vacua with the same scale factor $a$, but opposite $\dot a$.
The tunneling from one vacuum to the other provides a robust mechanism for
bounce universes; it always occurs for systems with positive energy density.
For suitable matter energy-momentum tensor we also construct cyclic universes.
Cosmological solutions that resemble the classical time crystals can be
constructed in massive gravity.
