Mass hierarchy and localization of gravity in extra time

We consider Randall–Sundrum model with localized gravity, replacing the extra compact space-like dimension by a time-like one. In this way the solution to the hierarchy problem can be reconciled with a correct cosmological expansion of the visible universe, just as a trivial result of the sign flip of cosmological constants in the bulk and on the 3-branes relative to the case of extra space-like dimension. Some phenomenological aspects of the proposed scenario related to the tachyonic nature of Kaluza–Klein states of graviton are also discussed.