Stable cosmic time crystals

Cosmological time crystals are created when a scalar field moves periodically through phase space in a spatially flat Friedmann-Robertson-Walker spacetime due to the presence of a limit cycle. All such cosmological time crystals in the literature suffer from gradient instabilities occurring at null energy condition violating phases where the square sound speed for cosmological perturbations becomes negative. Here we present stable cosmological time crystals. Our analysis suggests this new form of scalar matter-cosmic time crystals-may be considered as a physically viable cosmological matter source.