  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.
