Dark Energy from Time Crystals

In this work, we analyze a scalar field model which gives rise to stable bound states in field space characterized by nonzero motion that breaks the underlying time translation symmetry of its Hamiltonian, known as time crystals. We demonstrate that an ideal fluid made up of these time crystals behaves as phantom dark energy characterized by an equation of state $w\le -1$, speed of sound squared $c_s^2>0$, and nonnegative energy density $\rho \ge 0$.