Cosmological Time Crystals From Einstein-Cubic Gravities

TL;DR

This paper demonstrates that Einstein-Cubic gravity with specific Riemann invariants can produce classical time crystal dynamics, leading to bounce and cyclic universes through spontaneous symmetry breaking and tunneling mechanisms.

Contribution

It introduces a novel approach to realize classical time crystals in Einstein gravity by incorporating Riemann cubic invariants, enabling bounce and cyclic cosmological solutions.

Findings

Time reflection symmetry is spontaneously broken in two vacua with opposite a.

Tunneling between vacua leads to bounce universes with positive energy density.

Constructs cyclic universes with suitable matter energy-momentum tensor.

Abstract

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.